QuestionDecember 15, 2025

Express in simplest form: (x^2+3x-28)/(x^2)-16div (3x-6)/(x^2)+2x-8 (1 point) The simplest form is square

Express in simplest form: (x^2+3x-28)/(x^2)-16div (3x-6)/(x^2)+2x-8 (1 point) The simplest form is square
Express in simplest form: (x^2+3x-28)/(x^2)-16div (3x-6)/(x^2)+2x-8
(1 point)
The simplest form is square

Solution
4.1(208 votes)

Answer

\frac{x+7}{3} Explanation 1. Rewrite Division as Multiplication \frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} 2. Substitute and Multiply \frac{x^2+3x-28}{x^2-16} \times \frac{x^2+2x-8}{3x-6} 3. Factor All Expressions x^2+3x-28 = (x+7)(x-4) x^2-16 = (x+4)(x-4) x^2+2x-8 = (x+4)(x-2) 3x-6 = 3(x-2) 4. Substitute Factors \frac{(x+7)(x-4)}{(x+4)(x-4)} \times \frac{(x+4)(x-2)}{3(x-2)} 5. Cancel Common Factors (x-4), (x+4), and (x-2) cancel where possible: \frac{(x+7)\cancel{(x-4)}}{\cancel{(x+4)}\cancel{(x-4)}} \times \frac{\cancel{(x+4)}\cancel{(x-2)}}{3\cancel{(x-2)}} = \frac{x+7}{3}

Explanation

1. Rewrite Division as Multiplication<br /> $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$<br /><br />2. Substitute and Multiply<br /> $\frac{x^2+3x-28}{x^2-16} \times \frac{x^2+2x-8}{3x-6}$<br /><br />3. Factor All Expressions<br /> $x^2+3x-28 = (x+7)(x-4)$ <br />$x^2-16 = (x+4)(x-4)$ <br />$x^2+2x-8 = (x+4)(x-2)$ <br />$3x-6 = 3(x-2)$<br /><br />4. Substitute Factors<br /> $\frac{(x+7)(x-4)}{(x+4)(x-4)} \times \frac{(x+4)(x-2)}{3(x-2)}$<br /><br />5. Cancel Common Factors<br /> $(x-4)$, $(x+4)$, and $(x-2)$ cancel where possible: <br />$\frac{(x+7)\cancel{(x-4)}}{\cancel{(x+4)}\cancel{(x-4)}} \times \frac{\cancel{(x+4)}\cancel{(x-2)}}{3\cancel{(x-2)}} = \frac{x+7}{3}$
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