Algebra Class: Simplifying Expressions and Factoring

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Questions and Answers

What is the result of simplifying the expression $\frac{x^{2} + 3x - 2}{x^{2} + 3x - 10} + \frac{4x + 12}{x^{2} + 3x - 10}$?

$\frac{(x + 6)(x - 2)}{(x + 5)(x - 4)}$
$\frac{(x+4)(x+3)}{(x+5)(x+2)}$ (correct)
$\frac{x + 5}{x - 2}$
$\frac{x + 6}{x - 5}$

What is the result of simplifying the expression $\frac{x^{2} - 2x + 3}{x^{2} + 7x + 12} - \frac{x^{2} - 4x - 5}{x^{2} + 7x + 12}$?

$\frac{x + 4}{(x + 3)(x + 4)}$
$\frac{-x + 8}{x^{2} + 7x + 12}$
$\frac{-x + 4}{(x + 3)(x + 4)}$ (correct)
$\frac{-x + 2}{x^{2} + 7x + 12}$

What is the simplified form of $\frac{8}{3x + 24} + \frac{4}{3x + 24}$?

$\frac{4}{x + 8}$
$\frac{8}{3(x + 8)}$
$\frac{2}{3x + 24}$
$\frac{12}{3x + 24}$ (correct)

What is the outcome of simplifying $\frac{5x + 1}{x^{2} - 64} - \frac{4x - 7}{x^{2} - 64}$?

$\frac{9x + 8}{x^{2} - 64}$ (D) Signup and view all the answers

What is the simplified result of the expression $\frac{3x - 4}{x^{2} - 5x + 4} + \frac{3 - 2x}{x^{2} - 5x + 4}$?

$\frac{5}{(x - 1)(x - 4)}$ (B) Signup and view all the answers

What is the common denominator for the expressions in the equation $rac{-2x + 1}{x^{2} - 4} - rac{-3x - 1}{x^{2} - 4}$?

$x^{2} - 4$ (B) Signup and view all the answers

When combining $rac{8}{x} + rac{x + 9}{x}$, what type of expression does this result in?

An algebraic fraction (C) Signup and view all the answers

What is the result when simplifying the expression $rac{2x^{2} + 7x - 3}{x^{2} + 4x - 12} - rac{2x^{2} + 6x - 1}{x^{2} + 4x - 12}$?

$-x - 2$ (D) Signup and view all the answers

Which expression represents the sum of the fractions $rac{8}{3x + 24} + rac{4}{3x + 24}$ correctly simplified?

$rac{12}{3x + 24}$ (D) Signup and view all the answers

In the expression $rac{5x + 1}{x^{2} - 64} - rac{4x - 7}{x^{2} - 64}$, what is the process to combine the fractions?

Add the numerators directly since the denominators are the same (D) Signup and view all the answers

Flashcards

Adding or subtracting fractions with like denominators

Adding or subtracting fractions with the same denominator involves combining the numerators while keeping the denominator the same. For example, (\frac{a}{c} + \frac{b}{c} = \frac{a + b}{c}).

Subtracting rational expressions with like denominators

Subtracting rational expressions with the same denominator can be done by subtracting the numerators while retaining the common denominator. For example, (\frac{a}{c} - \frac{b}{c} = \frac{a - b}{c}).

Adding rational expressions

To add rational expressions, they must have the same denominator. If they don't, you need to find a common denominator before adding. For example, (\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}).

Simplifying expressions with like denominators

To simplify expressions involving adding or subtracting rational expressions with the same denominator, just combine the numerators and keep the common denominator. For example, (\frac{2x}{x-1} + \frac{x}{x-1} = \frac{2x + x}{x - 1} = \frac{3x}{x - 1}).