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College Algebra : Review and Other Topics

Study concepts, example questions & explanations for College Algebra

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Example Questions

Example Question #101 : Review And Other Topics

Simplify the following:

$\frac{3x^{2}+11x+10}{3x^{2}-x-10}$

Possible Answers:

$\frac{3x+2}{x-2}$

$\frac{x+2}{x-2}$

$\frac{x+2}{3x+5}$

$\frac{3x+5}{x-2}$

$\frac{x-2}{x+2}$

Correct answer:

$\frac{x+2}{x-2}$

Explanation:

The first step is to factor both polynomials

$\frac{3x^{2}+11x+10}{3x^{2}-x-10}$ becomes $\frac{(3x+5)(x+2)}{(3x+5)(x-2)}$

Now we cancel out any terms that are in both the numerator and denominator. Remember that any variables/numbers that are in parenthesis are considered a single term.

In this case, the common term is (3x+5)

Simplified, the equation is:

$\frac{x+2}{x-2}$

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Example Question #381 : College Algebra

Simplify the following:

$\frac{16x^{2}-9}{4x^{2}-17x-15}$

Possible Answers:

$\frac{(x-5)}{(4x-3)}$

$\frac{(4x-3)}{(x-5)}$

$\frac{(4x+3)}{(x+5)}$

$\frac{(4x-3)}{(x+5)}$

$\frac{(4x+3)}{(x-5)}$

Correct answer:

$\frac{(4x-3)}{(x-5)}$

Explanation:

The first step is to factor both polynomials

$\frac{16x^{2}-9}{4x^{2}-17x-15}$ becomes $\frac{(4x-3)(4x+3)}{(4x+3)(x-5)}$

Simplified, the equation is:

$\frac{(4x-3)}{(x-5)}$

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Example Question #382 : College Algebra

Simplify the following:

$\frac{x^{2}-1}{x^{2}+3x-4}$

Possible Answers:

$\frac{(x+1)}{(x-4)}$

$\frac{(x-1)}{(x-4)}$

$\frac{(x-1)}{(x+4)}$

$\frac{(x+1)}{(x+4)}$

$\frac{(x-2)}{(x+2)}$

Correct answer:

$\frac{(x+1)}{(x+4)}$

Explanation:

The first step is to factor both polynomials

$\frac{x^{2}-1}{x^{2}+3x-4}$ becomes $\frac{(x-1)(x+1)}{(x+4)(x-1)}$

$\frac{(x+1)}{(x+4)}$

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Example Question #383 : College Algebra

Simplify the following:

$\frac{12x^{2}+11x+2}{6x^{2}+x-2}$

Possible Answers:

$\frac{(4x+1)}{(3x+2)}$

$\frac{(4x-1)}{(2x-1)}$

$\frac{(4x+1)}{(2x-1)}$

$\frac{(3x+2)}{(2x-1)}$

$\frac{(4x+1)}{(3x-1)}$

Correct answer:

$\frac{(4x+1)}{(2x-1)}$

Explanation:

The first step is to factor both polynomials

$\frac{12x^{2}+11x+2}{6x^{2}+x-2}$ becomes $\frac{(3x+2)(4x+1)}{(2x-1)(3x+2)}$

$\frac{(4x+1)}{(2x-1)}$

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Example Question #384 : College Algebra

Simplify the following:

$\frac{2x^{2}+x-15}{3x^{2}+4x-15}$

Possible Answers:

$\frac{(3x+5)}{(3x-5)}$

$\frac{(2x+5)}{(3x-5)}$

$\frac{(2x-5)}{(3x+5)}$

$\frac{(2x-5)}{(2x+5)}$

$\frac{(2x-5)}{(3x-5)}$

Correct answer:

$\frac{(2x-5)}{(3x-5)}$

Explanation:

The first step is to factor both polynomials

$\frac{2x^{2}+x-15}{3x^{2}+4x-15}$ becomes $\frac{(2x-5)(x+3)}{(3x-5)(x+3)}$

$\frac{(2x-5)}{(3x-5)}$

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Example Question #385 : College Algebra

Simplify the following:

$\frac{5x^{2}+31x+6}{5x^{2}-29x-6}$

Possible Answers:

$\frac{(x+6)}{(x-6)}$

$\frac{(5x+6)}{(3x-6)}$

$\frac{(5x+6)}{(x-6)}$

$\frac{(x-6)}{(x+6)}$

$\frac{(x+6)}{(5x-6)}$

Correct answer:

$\frac{(x+6)}{(x-6)}$

Explanation:

The first step is to factor both polynomials

$\frac{5x^{2}+31x+6}{5x^{2}-29x-6}$ becomes $\frac{(5x+1)(x+6)}{(5x+1)(x-6)}$

$\frac{(x+6)}{(x-6)}$

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Example Question #102 : Review And Other Topics

Simplify the following:

$\frac{6x^{2}-x-1}{12x^{2}+x-1}$

Possible Answers:

$\frac{(2x-1)}{(4x-1)}$

$\frac{(3x+1)}{(3x-1)}$

$\frac{(2x-1)}{(3x+1)}$

$\frac{(2x+1)}{(4x-1)}$

$\frac{(3x+1)}{(4x-1)}$

Correct answer:

$\frac{(2x-1)}{(4x-1)}$

Explanation:

The first step is to factor both polynomials

$\frac{6x^{2}-x-1}{12x^{2}+x-1}$ becomes $\frac{(3x+1)(2x-1)}{(3x+1)(4x-1)}$

$\frac{(2x-1)}{(4x-1)}$

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Example Question #382 : College Algebra

Simplify the following:

$\frac{16x^{2}-1}{4x^{2}-15x-4}$

Possible Answers:

$\frac{(4x-1)}{(x+4)}$

$\frac{(4x-1)}{(x-4)}$

$\frac{(4x+1)}{(x-4)}$

$\frac{(4x-1)}{(4x+1)}$

$\frac{(4x+1)}{(x+4)}$

Correct answer:

$\frac{(4x-1)}{(x-4)}$

Explanation:

The first step is to factor both polynomials

$\frac{16x^{2}-1}{4x^{2}-15x-4}$ becomes $\frac{(4x+1)(4x-1)}{(4x+1)(x-4)}$

$\frac{(4x-1)}{(x-4)}$

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Example Question #13 : Rational Expressions

Simplify the following:

$\frac{2x^{2}+13x-7}{2x^{2}-17x+8}$

Possible Answers:

$\frac{(x+8)}{(x-7)}$

$\frac{(x+7)}{(x-8)}$

$\frac{(x-7)}{(x-8)}$

$\frac{(x-7)}{(x+8)}$

$\frac{(x+7)}{(x+8)}$

Correct answer:

$\frac{(x+7)}{(x-8)}$

Explanation:

The first step is to factor both polynomials

$\frac{2x^{2}+13x-7}{2x^{2}-17x+8}$ becomes $\frac{(2x-1)(x+7)}{(2x-1)(x-8)}$

Simplified, the equation is:

$\frac{(x+7)}{(x-8)}$

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Example Question #14 : Rational Expressions

Simplify the given expression:

$\frac{x^2+4x-12}{2x+12}$

Possible Answers:

$\frac{2}{x+2}$

$\frac{x+6}{2}$

x-2

$\frac{x-2}{2}$

$\frac{1}{x+6}$

Correct answer:

$\frac{x-2}{2}$

Explanation:

First we want to factor both the numerator and denominator:

$\frac{x^2+4x-12}{2x+12}$

For the numerator, we can use the quadratic formula:

$x=\frac{-(4)\pm \sqrt{4^{2}-4(1)(-12)}}{2(1)}$

$\\x=\frac{-4\pm \sqrt{16+48}}{2}\\x=\frac{-4\pm\sqrt{64}}{2}\\x=\frac{-4\pm8}{2}$

$\\x=\frac{-12}{2}\;or\;x=\frac{4}{2}\\\\x=-6\;or\;x=2$

For the denominator, we only need to factor out the , leaving us with the given factored expression:

$\frac{(x+6)(x-2)}{2(x+6)}$

Then we cancel out like terms, giving us a simplified expression:

$\frac{x-2}{2}$

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College Algebra : Review and Other Topics

Study concepts, example questions & explanations for College Algebra

All College Algebra Resources

Example Questions

Example Question #101 : Review And Other Topics

Example Question #381 : College Algebra

Example Question #382 : College Algebra

Example Question #383 : College Algebra

Example Question #384 : College Algebra

Example Question #385 : College Algebra

Example Question #102 : Review And Other Topics

Example Question #382 : College Algebra

Example Question #13 : Rational Expressions

Example Question #14 : Rational Expressions

All College Algebra Resources

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