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Algebra II : Definition of Rational Expression

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Example Questions

Example Question #1 : Understanding Rational Expressions

Which of the following fractions is NOT equivalent to $- \frac{x-5}{2x + 3}$ ?

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

We know that $-\frac{a}{b}$ is equivalent to $\frac{-a}{b}$ or $\frac{a}{-b}$ .

By this property, there is no way to get $\frac{x+5}{2x+3}$ from $-\frac{x-5}{2x+3}$ .

Therefore the correct answer is $\frac{x+5}{2x+3}$ .

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Example Question #1 : Rational Expressions

Determine the domain of

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

Possible Answers:

$x\neq1$

All real numbers

x=1

$x\neq-1$

Correct answer:

$x\neq1$

Explanation:

Because the denominator cannot be zero, the domain is all other numbers except for 1, or

$x\neq1$

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Example Question #3 : Rational Expressions

Simplify:

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

Possible Answers:

x-1

$\frac{x+2}{x+1}$

$\frac{x-1}{x+2}$

$\frac{x+2}{x-1}$

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

Correct answer:

$\frac{x-1}{x+2}$

Explanation:

This problem is a lot simpler if we factor all the expressions involved before proceeding:

$\frac{x^2-1}{x^2+4x+2}\div\frac{x^2+2x+1}{x^2+3x+2} \vspace{5mm}\\ = \frac{(x+1)(x-1)}{(x+2)(x+2)}\div\frac{(x+1)(x+1)}{(x+2)(x+1)}$

Next let's remember how we divide one fraction by another—by multiplying by the reciprocal:

$\frac{(x+1)(x-1)}{(x+2)(x+2)}\div\frac{(x+1)(x+1)}{(x+2)(x+1)} \vspace{5mm}\\ = \frac{(x+1)(x-1)}{(x+2)(x+2)}\times\frac{(x+2)(x+1)}{(x+1)(x+1)}$

In this form, we can see that a lot of terms are going to start canceling with each other. All that we're left with is just $\frac{x-1}{x+2}$ .

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Example Question #4 : Rational Expressions

Which of the following is the best definition of a rational expression?

Possible Answers:

$\textup{The ratio of any two real numbers.}$

$\textup{The ratio of any two imaginary numbers.}$

$\textup{The ratio of two fractions that may have a zero denominator.}$

$\textup{The ratio of two polynomials that cannot have a zero denominator.}$

$\textup{The ratio of two polynomials that must be different from each other.}$

Correct answer:

$\textup{The ratio of two polynomials that cannot have a zero denominator.}$

Explanation:

The rational expression is a ratio of two polynomials.

$\frac{A(x)}{B(x)}$

The denominator cannot be zero.

An example of a rational expression is:

$\frac{x^2+x-5}{x+8}$

The answer is:

$\textup{The ratio of two polynomials that cannot have a zero denominator.}$

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Algebra II : Definition of Rational Expression

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #1 : Understanding Rational Expressions

Example Question #1 : Rational Expressions

Example Question #3 : Rational Expressions

Example Question #4 : Rational Expressions

All Algebra II Resources

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