QuestionJuly 20, 2025

Simplify the expression (4x-8)/(x^2)-4/(4)/(-2x-4) square

Simplify the expression (4x-8)/(x^2)-4/(4)/(-2x-4) square
Simplify the expression
(4x-8)/(x^2)-4/(4)/(-2x-4)
square

Solution
4.1(158 votes)

Answer

\(\frac{-2}{x+2}\) Explanation 1. Simplify the expression The given expression is \( \frac{4x-8}{x^2-4} \div \frac{4}{-2x-4} \). To simplify, multiply by the reciprocal: \( \frac{4x-8}{x^2-4} \times \frac{-2x-4}{4} \). 2. Factor the numerators and denominators Factor ( 4x-8 = 4(x-2) ), \( x^2-4 = (x-2)(x+2) \), and ( -2x-4 = -2(x+2) ). 3. Substitute factored forms Substitute to get \( \frac{4(x-2)}{(x-2)(x+2)} \times \frac{-2(x+2)}{4} \). 4. Cancel common factors Cancel ( 4 ) and ( (x-2) ), ( (x+2) ) from numerator and denominator: \( \frac{1}{x+2} \times (-2) \). 5. Multiply remaining terms Multiply to get \( \frac{-2}{x+2} \).

Explanation

1. Simplify the expression<br /> The given expression is \( \frac{4x-8}{x^2-4} \div \frac{4}{-2x-4} \). To simplify, multiply by the reciprocal: \( \frac{4x-8}{x^2-4} \times \frac{-2x-4}{4} \).<br /><br />2. Factor the numerators and denominators<br /> Factor ( 4x-8 = 4(x-2) ), \( x^2-4 = (x-2)(x+2) \), and ( -2x-4 = -2(x+2) ).<br /><br />3. Substitute factored forms<br /> Substitute to get \( \frac{4(x-2)}{(x-2)(x+2)} \times \frac{-2(x+2)}{4} \).<br /><br />4. Cancel common factors<br /> Cancel ( 4 ) and ( (x-2) ), ( (x+2) ) from numerator and denominator: \( \frac{1}{x+2} \times (-2) \).<br /><br />5. Multiply remaining terms<br /> Multiply to get \( \frac{-2}{x+2} \).
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