simplify $\frac{\frac{x + 2}{x^{2}+2x - 3}}{\frac{x + 2}{x^{2}-x}}$.\n$\frac{1}{x^{2}+3x}$\n$\frac{x}{x +…

simplify $\frac{\frac{x + 2}{x^{2}+2x - 3}}{\frac{x + 2}{x^{2}-x}}$.\n$\frac{1}{x^{2}+3x}$\n$\frac{x}{x + 3}$\n$\frac{x + 3}{x}$\n$x^{2}+3x$\ndone

simplify $\frac{\frac{x + 2}{x^{2}+2x - 3}}{\frac{x + 2}{x^{2}-x}}$.\n$\frac{1}{x^{2}+3x}$\n$\frac{x}{x + 3}$\n$\frac{x + 3}{x}$\n$x^{2}+3x$\ndone

Answer

Explanation:

Step1: Factor the denominators

Factor $x^{2}+2x - 3=(x + 3)(x - 1)$ and $x^{2}-x=x(x - 1)$. The expression becomes $\frac{\frac{x + 2}{(x + 3)(x - 1)}}{\frac{x + 2}{x(x - 1)}}$.

Step2: Use the rule of dividing fractions

Dividing by a fraction is the same as multiplying by its reciprocal. So $\frac{\frac{x + 2}{(x + 3)(x - 1)}}{\frac{x + 2}{x(x - 1)}}=\frac{x + 2}{(x + 3)(x - 1)}\times\frac{x(x - 1)}{x + 2}$.

Step3: Cancel out common factors

Cancel out the common factors $(x + 2)$ and $(x - 1)$ in the numerator and denominator. We get $\frac{x}{x + 3}$.

Answer:

$\frac{x}{x + 3}$