Exam 7: Rational Expressions and Equations

Solve the problem. -Martha can rake the leaves in her yard in 2 hours. Her brother can do the job in 3 hours. How long will it take them to do the job working together?

(Multiple Choice)

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Question 161

Solve the problem. -A boat can go 350 miles downstream in the same time it can go 280 miles upstream. The speed of the current is 9 miles per hour. Find the speed of the boat in still water.

(Multiple Choice)

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Question 162

Simplify the rational expression. (Assume the denominator is nonzero.) - $\frac { 9 x ^ { 2 } - 99 x + 270 } { 12 x ^ { 2 } - 108 x + 216 }$

(Multiple Choice)

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Question 163

Simplify the rational expression. (Assume the denominator is nonzero.) - $\frac { x ^ { 2 } + 8 x + 12 } { x ^ { 2 } + 9 x + 14 } \cdot \frac { x ^ { 2 } + 7 x } { x ^ { 2 } + 2 x - 24 }$

(Multiple Choice)

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Question 164

Divide. - $\frac { x + 4 } { x - 7 } \div \frac { x + 3 } { x - 5 }$

(Multiple Choice)

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Question 165

Simplify the complex fraction. - $P = \frac { A } { 1 + r t }$ for $r$

(Multiple Choice)

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Question 166

Evaluate the rational function. - $r ( x ) = \frac { x ^ { 2 } - 11 x + 24 } { x ^ { 2 } - 7 x + 12 } , r ( 3 )$

(Multiple Choice)

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Question 167

Find the domain of the rational function. - $r ( x ) = \frac { x ^ { 2 } - 36 } { x ^ { 2 } - 6 x - 16 }$

(Multiple Choice)

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Question 168

Simplify the complex fraction. - $\frac { 6 + \frac { 1 } { 3 } } { 4 - \frac { 2 } { 9 } }$

(Multiple Choice)

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Question 169

Add or subtract. - $\frac { x ^ { 2 } - 7 x - 7 } { x - 3 } + \frac { x ^ { 2 } - 3 x - 19 } { 3 - x }$

(Multiple Choice)

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Question 170

Find the LCD of the given rational expressions. - $\frac { 1 } { x ^ { 2 } + 4 x + 4 } , \frac { x - 7 } { x ^ { 2 } + 2 x }$

(Multiple Choice)

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Question 171

Find the LCD of the given rational expressions. - $\frac { 9 } { 4 x } , \frac { 4 } { 6 x ^ { 2 } }$

(Multiple Choice)

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Question 172

Simplify the complex fraction. - $\frac { \frac { x ^ { 2 } - 1 } { x ^ { 2 } + 9 x + 8 } } { \frac { x ^ { 2 } + 6 x - 16 } { x ^ { 2 } + 4 x - 32 } }$

(Multiple Choice)

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Question 173

Determine whether the two binomials are or are not opposites. -6x + 7 and -6x + 7

(Multiple Choice)

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Question 174

Divide. - $\frac { x ^ { 2 } - 3 x + 2 } { x ^ { 2 } + 4 x + 4 } \div \frac { x ^ { 2 } - 2 x + 1 } { x ^ { 2 } - 8 x + 12 }$

(Multiple Choice)

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Question 175

Subtract. - $\frac { 4 x } { x ^ { 2 } - 5 x + 6 } - \frac { 16 } { x ^ { 2 } - 6 x + 8 }$

(Multiple Choice)

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Question 176

Determine whether the two binomials are or are not opposites. --7x - 3 and 7x + 3

(Multiple Choice)

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Question 177

Add. - $\frac { x + 2 } { x ^ { 2 } + 12 x + 35 } + \frac { 3 x - 5 } { x ^ { 2 } + 9 x + 20 }$

(Multiple Choice)

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Question 178

Find the missing numerator and denominator. - $\frac { x ^ { 2 } } { x ^ { 2 } - 5 x - 24 } \cdot \frac { ? } { ? } = \frac { x ( x + 8 ) } { 4 ( x + 3 ) }$

(Multiple Choice)

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Question 179

Find the domain of the rational function. - $r ( x ) = \frac { x ^ { 2 } - 3 x } { x ^ { 2 } - 2 x - 15 }$

(Multiple Choice)

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Question 180

Solve the problem. -Martha can rake the leaves in her yard in 2 hours. Her brother can do the job in 3 hours. How long will it take them to do the job working together?

Solve the problem. -A boat can go 350 miles downstream in the same time it can go 280 miles upstream. The speed of the current is 9 miles per hour. Find the speed of the boat in still water.

Simplify the rational expression. (Assume the denominator is nonzero.) - $\frac { 9 x ^ { 2 } - 99 x + 270 } { 12 x ^ { 2 } - 108 x + 216 }$

Simplify the rational expression. (Assume the denominator is nonzero.) - $\frac { x ^ { 2 } + 8 x + 12 } { x ^ { 2 } + 9 x + 14 } \cdot \frac { x ^ { 2 } + 7 x } { x ^ { 2 } + 2 x - 24 }$

Divide. - $\frac { x + 4 } { x - 7 } \div \frac { x + 3 } { x - 5 }$

Simplify the complex fraction. - $P = \frac { A } { 1 + r t }$ for $r$

Evaluate the rational function. - $r ( x ) = \frac { x ^ { 2 } - 11 x + 24 } { x ^ { 2 } - 7 x + 12 } , r ( 3 )$

Find the domain of the rational function. - $r ( x ) = \frac { x ^ { 2 } - 36 } { x ^ { 2 } - 6 x - 16 }$

Simplify the complex fraction. - $\frac { 6 + \frac { 1 } { 3 } } { 4 - \frac { 2 } { 9 } }$

Add or subtract. - $\frac { x ^ { 2 } - 7 x - 7 } { x - 3 } + \frac { x ^ { 2 } - 3 x - 19 } { 3 - x }$

Find the LCD of the given rational expressions. - $\frac { 1 } { x ^ { 2 } + 4 x + 4 } , \frac { x - 7 } { x ^ { 2 } + 2 x }$

Find the LCD of the given rational expressions. - $\frac { 9 } { 4 x } , \frac { 4 } { 6 x ^ { 2 } }$

Simplify the complex fraction. - $\frac { \frac { x ^ { 2 } - 1 } { x ^ { 2 } + 9 x + 8 } } { \frac { x ^ { 2 } + 6 x - 16 } { x ^ { 2 } + 4 x - 32 } }$

Determine whether the two binomials are or are not opposites. -6x + 7 and -6x + 7

Divide. - $\frac { x ^ { 2 } - 3 x + 2 } { x ^ { 2 } + 4 x + 4 } \div \frac { x ^ { 2 } - 2 x + 1 } { x ^ { 2 } - 8 x + 12 }$

Subtract. - $\frac { 4 x } { x ^ { 2 } - 5 x + 6 } - \frac { 16 } { x ^ { 2 } - 6 x + 8 }$

Determine whether the two binomials are or are not opposites. --7x - 3 and 7x + 3

Add. - $\frac { x + 2 } { x ^ { 2 } + 12 x + 35 } + \frac { 3 x - 5 } { x ^ { 2 } + 9 x + 20 }$

Find the missing numerator and denominator. - $\frac { x ^ { 2 } } { x ^ { 2 } - 5 x - 24 } \cdot \frac { ? } { ? } = \frac { x ( x + 8 ) } { 4 ( x + 3 ) }$

Find the domain of the rational function. - $r ( x ) = \frac { x ^ { 2 } - 3 x } { x ^ { 2 } - 2 x - 15 }$

Review of Real Numbers

Linear Equations

Graphing Linear Equations

Systems of Equations

Exponents and Polynomials

Factoring and Quadratic Equations

A Transition

Radical Expressions and Equations

Quadratic Equations

Functions

Logarithmic and Exponential Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 7: Rational Expressions and Equations

Solve the problem. -Martha can rake the leaves in her yard in 2 hours. Her brother can do the job in 3 hours. How long will it take them to do the job working together?

Solve the problem. -A boat can go 350 miles downstream in the same time it can go 280 miles upstream. The speed of the current is 9 miles per hour. Find the speed of the boat in still water.

Simplify the rational expression. (Assume the denominator is nonzero.) - 9x2−99x+27012x2−108x+216\frac { 9 x ^ { 2 } - 99 x + 270 } { 12 x ^ { 2 } - 108 x + 216 }12x2−108x+2169x2−99x+270​

Simplify the rational expression. (Assume the denominator is nonzero.) - x2+8x+12x2+9x+14⋅x2+7xx2+2x−24\frac { x ^ { 2 } + 8 x + 12 } { x ^ { 2 } + 9 x + 14 } \cdot \frac { x ^ { 2 } + 7 x } { x ^ { 2 } + 2 x - 24 }x2+9x+14x2+8x+12​⋅x2+2x−24x2+7x​

Divide. - x+4x−7÷x+3x−5\frac { x + 4 } { x - 7 } \div \frac { x + 3 } { x - 5 }x−7x+4​÷x−5x+3​

Simplify the complex fraction. - P=A1+rtP = \frac { A } { 1 + r t }P=1+rtA​ for rrr

Evaluate the rational function. - r(x)=x2−11x+24x2−7x+12,r(3)r ( x ) = \frac { x ^ { 2 } - 11 x + 24 } { x ^ { 2 } - 7 x + 12 } , r ( 3 )r(x)=x2−7x+12x2−11x+24​,r(3)

Find the domain of the rational function. - r(x)=x2−36x2−6x−16r ( x ) = \frac { x ^ { 2 } - 36 } { x ^ { 2 } - 6 x - 16 }r(x)=x2−6x−16x2−36​

Simplify the complex fraction. - 6+134−29\frac { 6 + \frac { 1 } { 3 } } { 4 - \frac { 2 } { 9 } }4−92​6+31​​

Add or subtract. - x2−7x−7x−3+x2−3x−193−x\frac { x ^ { 2 } - 7 x - 7 } { x - 3 } + \frac { x ^ { 2 } - 3 x - 19 } { 3 - x }x−3x2−7x−7​+3−xx2−3x−19​

Find the LCD of the given rational expressions. - 1x2+4x+4,x−7x2+2x\frac { 1 } { x ^ { 2 } + 4 x + 4 } , \frac { x - 7 } { x ^ { 2 } + 2 x }x2+4x+41​,x2+2xx−7​

Find the LCD of the given rational expressions. - 94x,46x2\frac { 9 } { 4 x } , \frac { 4 } { 6 x ^ { 2 } }4x9​,6x24​

Simplify the complex fraction. - x2−1x2+9x+8x2+6x−16x2+4x−32\frac { \frac { x ^ { 2 } - 1 } { x ^ { 2 } + 9 x + 8 } } { \frac { x ^ { 2 } + 6 x - 16 } { x ^ { 2 } + 4 x - 32 } }x2+4x−32x2+6x−16​x2+9x+8x2−1​​

Determine whether the two binomials are or are not opposites. -6x + 7 and -6x + 7

Divide. - x2−3x+2x2+4x+4÷x2−2x+1x2−8x+12\frac { x ^ { 2 } - 3 x + 2 } { x ^ { 2 } + 4 x + 4 } \div \frac { x ^ { 2 } - 2 x + 1 } { x ^ { 2 } - 8 x + 12 }x2+4x+4x2−3x+2​÷x2−8x+12x2−2x+1​

Subtract. - 4xx2−5x+6−16x2−6x+8\frac { 4 x } { x ^ { 2 } - 5 x + 6 } - \frac { 16 } { x ^ { 2 } - 6 x + 8 }x2−5x+64x​−x2−6x+816​

Determine whether the two binomials are or are not opposites. --7x - 3 and 7x + 3

Add. - x+2x2+12x+35+3x−5x2+9x+20\frac { x + 2 } { x ^ { 2 } + 12 x + 35 } + \frac { 3 x - 5 } { x ^ { 2 } + 9 x + 20 }x2+12x+35x+2​+x2+9x+203x−5​

Find the missing numerator and denominator. - x2x2−5x−24⋅??=x(x+8)4(x+3)\frac { x ^ { 2 } } { x ^ { 2 } - 5 x - 24 } \cdot \frac { ? } { ? } = \frac { x ( x + 8 ) } { 4 ( x + 3 ) }x2−5x−24x2​⋅??​=4(x+3)x(x+8)​

Find the domain of the rational function. - r(x)=x2−3xx2−2x−15r ( x ) = \frac { x ^ { 2 } - 3 x } { x ^ { 2 } - 2 x - 15 }r(x)=x2−2x−15x2−3x​

Review of Real Numbers

Linear Equations

Graphing Linear Equations

Systems of Equations

Exponents and Polynomials

Factoring and Quadratic Equations

A Transition

Radical Expressions and Equations

Quadratic Equations

Functions

Logarithmic and Exponential Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Simplify the rational expression. (Assume the denominator is nonzero.) - $\frac { 9 x ^ { 2 } - 99 x + 270 } { 12 x ^ { 2 } - 108 x + 216 }$

Simplify the rational expression. (Assume the denominator is nonzero.) - $\frac { x ^ { 2 } + 8 x + 12 } { x ^ { 2 } + 9 x + 14 } \cdot \frac { x ^ { 2 } + 7 x } { x ^ { 2 } + 2 x - 24 }$

Divide. - $\frac { x + 4 } { x - 7 } \div \frac { x + 3 } { x - 5 }$

Simplify the complex fraction. - $P = \frac { A } { 1 + r t }$ for $r$

Evaluate the rational function. - $r ( x ) = \frac { x ^ { 2 } - 11 x + 24 } { x ^ { 2 } - 7 x + 12 } , r ( 3 )$

Find the domain of the rational function. - $r ( x ) = \frac { x ^ { 2 } - 36 } { x ^ { 2 } - 6 x - 16 }$

Simplify the complex fraction. - $\frac { 6 + \frac { 1 } { 3 } } { 4 - \frac { 2 } { 9 } }$

Add or subtract. - $\frac { x ^ { 2 } - 7 x - 7 } { x - 3 } + \frac { x ^ { 2 } - 3 x - 19 } { 3 - x }$

Find the LCD of the given rational expressions. - $\frac { 1 } { x ^ { 2 } + 4 x + 4 } , \frac { x - 7 } { x ^ { 2 } + 2 x }$

Find the LCD of the given rational expressions. - $\frac { 9 } { 4 x } , \frac { 4 } { 6 x ^ { 2 } }$

Simplify the complex fraction. - $\frac { \frac { x ^ { 2 } - 1 } { x ^ { 2 } + 9 x + 8 } } { \frac { x ^ { 2 } + 6 x - 16 } { x ^ { 2 } + 4 x - 32 } }$

Divide. - $\frac { x ^ { 2 } - 3 x + 2 } { x ^ { 2 } + 4 x + 4 } \div \frac { x ^ { 2 } - 2 x + 1 } { x ^ { 2 } - 8 x + 12 }$

Subtract. - $\frac { 4 x } { x ^ { 2 } - 5 x + 6 } - \frac { 16 } { x ^ { 2 } - 6 x + 8 }$

Add. - $\frac { x + 2 } { x ^ { 2 } + 12 x + 35 } + \frac { 3 x - 5 } { x ^ { 2 } + 9 x + 20 }$

Find the missing numerator and denominator. - $\frac { x ^ { 2 } } { x ^ { 2 } - 5 x - 24 } \cdot \frac { ? } { ? } = \frac { x ( x + 8 ) } { 4 ( x + 3 ) }$

Find the domain of the rational function. - $r ( x ) = \frac { x ^ { 2 } - 3 x } { x ^ { 2 } - 2 x - 15 }$