QuestionDecember 12, 2025

23 (x+1)/(x^2)-16-(x)/(x^2)+7x+12

23 (x+1)/(x^2)-16-(x)/(x^2)+7x+12
23 (x+1)/(x^2)-16-(x)/(x^2)+7x+12

Solution
4.3(357 votes)

Answer

\frac{8x+3}{(x-4)(x+4)(x+3)} Explanation 1. Factor denominators x^2-16 = (x-4)(x+4), x^2+7x+12 = (x+3)(x+4). 2. Find common denominator Common denominator is (x-4)(x+4)(x+3). 3. Rewrite fractions with common denominator \frac{x+1}{(x-4)(x+4)} = \frac{(x+1)(x+3)}{(x-4)(x+4)(x+3)}; \frac{x}{(x+3)(x+4)} = \frac{x(x-4)}{(x-4)(x+4)(x+3)}. 4. Combine numerators (x+1)(x+3) - x(x-4) = (x^2+4x+3) - (x^2-4x) = 8x + 3. 5. Write final simplified form \frac{8x+3}{(x-4)(x+4)(x+3)}.

Explanation

1. Factor denominators<br /> $x^2-16 = (x-4)(x+4)$, $x^2+7x+12 = (x+3)(x+4)$.<br />2. Find common denominator<br /> Common denominator is $(x-4)(x+4)(x+3)$.<br />3. Rewrite fractions with common denominator<br /> $\frac{x+1}{(x-4)(x+4)} = \frac{(x+1)(x+3)}{(x-4)(x+4)(x+3)}$; $\frac{x}{(x+3)(x+4)} = \frac{x(x-4)}{(x-4)(x+4)(x+3)}$.<br />4. Combine numerators<br /> $(x+1)(x+3) - x(x-4) = (x^2+4x+3) - (x^2-4x) = 8x + 3$.<br />5. Write final simplified form<br /> $\frac{8x+3}{(x-4)(x+4)(x+3)}$.
Click to rate: