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Algebra Class: Simplifying Expressions and Factoring

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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 $\frac{5x + 1}{x^{2} - 64} - \frac{4x - 7}{x^{2} - 64}$?

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

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

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

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

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

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

$-x - 2$ Signup and view all the answers

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

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

Study Notes

Simplifying Expressions

Simplify expressions involving polynomials.
Example 1: (x²+3x-2) + (4x+12) / (x²+3x-10) = 1
Example 2: (x²-2x+3) + (x²-4x-5) / (x²+7x+12) = 1
Example 3: (x²+8x+9) / (x+9) = x+9
Example 4: (3x²+24) + (3x+24) / (-2x+1) - (3x+1) = 1

Factoring Expressions

Factoring expressions with quadratic and linear terms.
Example 5: (5x+1) / (x²-4) = (5x+1) / (x-2)(x+2)
Example 6: (x²-64) / (x²-64) = 1

Rational Expressions

Simplify rational expressions.
Example 7: (2x²+7x-3 + 2x²+6x−1 ) / (x²+4x−12) = (4x²+13x-4) / (x²+4x−12)
Example 8: (3x-4) / (x²-5x+4) + (3-2x) / (x²-5x+4) = (x-1)/ (x-4)(x-1) = 1/(x-4)

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Description

This quiz focuses on simplifying polynomial expressions and factoring quadratic and linear terms. You will encounter various examples showcasing the simplification of rational expressions and polynomial operations. Test your knowledge and skills to master these algebraic concepts.