Simplify Rational Expressions
-$$\frac { x ^ { 2 } + 8 x + 15 } { x ^ { 2 } + 14 x + 45 }$$

Question

Quizplus · Accepted Answer

To simplify the given rational expression, factor both the numerator and the denominator. The numerator $x^2 + 8x + 15$ factors into $(x + 3)(x + 5)$, and the denominator $x^2 + 14x + 45$ factors into $(x + 5)(x + 9)$. After factoring, the expression simplifies to $\frac{x + 3}{x + 9}$, with the restriction that $x \neq -5$ (from the factor that cancels out) and $x \neq -9$ (to avoid division by zero).

Simplify Rational Expressions - x2+8x+15x2+14x+45\frac { x ^ { 2 } + 8 x + 15 } { x ^ { 2 } + 14 x + 45 }x2+14x+45x2+8x+15​

Simplify Rational Expressions
- $\frac { x ^ { 2 } + 8 x + 15 } { x ^ { 2 } + 14 x + 45 }$