Back to Tutor Intake Assessment: Perform rational expression operations

HSA.APR.D.7 Tutor Intake — Rational Expression Arithmetic

This short check helps your tutor understand where to start with rational expression arithmetic. Answer each question on your own without help. If you are unsure, give your best try. (Note: This is an advanced topic marked (+).)

Grade 10·5 problems·~12 min·Common Core Math - HS Algebra·standard·hsa-apr-d-7

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Concepts

What is the domain of $\dfrac{x + 2}{x^2 - 5x + 6}$ ?

All real numbers except $x = -2$ .

All real numbers except $x = 2$ and $x = 3$ .

All real numbers except $x = -2$ and $x = 5$ .

All real numbers; the expression is always defined.

Simplify $\dfrac{3x + 2}{x^2 - 1} + \dfrac{x - 5}{x^2 - 1}$ .

$\dfrac{4x - 3}{x^2 - 1}$

$\dfrac{4x - 3}{2(x^2 - 1)}$

$\dfrac{3x - 3}{x^2 - 1}$

$\dfrac{4x + 7}{x^2 - 1}$

Procedures

Multiply and simplify:
$\dfrac{x^2 - 9}{x + 4} \cdot \dfrac{2x + 8}{x + 3}$ .

The simplified result is $2(x - 3)$ for $x \neq -3$ and $x \neq -4$ .
Enter the coefficient of $x$ in the expanded simplified form.

Add the rational expressions:
$\dfrac{2}{x - 3} + \dfrac{5}{x + 1}$ .

The result has the form $\dfrac{Ax + B}{(x-3)(x+1)}$ .
Enter the value of $A$ (the coefficient of $x$ in the numerator).

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