Add and Subtract Rational Expressions
-$$\frac { x } { x ^ { 2 } - 16 } - \frac { 8 } { x ^ { 2 } + 5 x + 4 }$$

Question

Quizplus · Accepted Answer

To add or subtract rational expressions, first factor the denominators. The first denominator $x^2 - 16$ factors into $(x - 4)(x + 4)$, and the second denominator $x^2 + 5x + 4$ factors into $(x + 4)(x + 1)$. The least common denominator (LCD) is $(x - 4)(x + 4)(x + 1)$. Adjusting the numerators to have the same denominator, the expression becomes $\frac{x(x + 1) - 8(x - 4)}{(x - 4)(x + 4)(x + 1)}$, which simplifies to $\frac{x^2 + x - 8x + 32}{(x - 4)(x + 4)(x + 1)} = \frac{x^2 - 7x + 32}{(x - 4)(x + 4)(x + 1)}$.

Add and Subtract Rational Expressions - xx2−16−8x2+5x+4\frac { x } { x ^ { 2 } - 16 } - \frac { 8 } { x ^ { 2 } + 5 x + 4 }x2−16x​−x2+5x+48​

Add and Subtract Rational Expressions
- $\frac { x } { x ^ { 2 } - 16 } - \frac { 8 } { x ^ { 2 } + 5 x + 4 }$