simplify: $\frac{x}{x - 3}-\frac{3}{x + 4}+\frac{7}{x^{2}+x - 12}$\nrewrite the expression using the…

simplify: $\frac{x}{x - 3}-\frac{3}{x + 4}+\frac{7}{x^{2}+x - 12}$\nrewrite the expression using the lcd:\n$\frac{x(x + 4)-3(x - 3)+7}{(x - 3)(x + 4)}$\n$\frac{x(x + 4)+3(x - 3)+7}{(x - 3)(x + 4)}$\n$\frac{x(x + 4)+3(x - 3)-7}{(x - 3)(x + 4)}$\ndone

simplify: $\frac{x}{x - 3}-\frac{3}{x + 4}+\frac{7}{x^{2}+x - 12}$\nrewrite the expression using the lcd:\n$\frac{x(x + 4)-3(x - 3)+7}{(x - 3)(x + 4)}$\n$\frac{x(x + 4)+3(x - 3)+7}{(x - 3)(x + 4)}$\n$\frac{x(x + 4)+3(x - 3)-7}{(x - 3)(x + 4)}$\ndone

Answer

Explanation:

Step1: Factor the denominator of the third term

$x^2 + x - 12 = (x - 3)(x + 4)$

Step2: Identify the least common denominator (LCD)

LCD is $(x - 3)(x + 4)$

Step3: Rewrite each term with LCD as the denominator

$\frac{x}{x - 3} = \frac{x(x + 4)}{(x - 3)(x + 4)}$, $\frac{3}{x + 4} = \frac{3(x - 3)}{(x - 3)(x + 4)}$, $\frac{7}{(x - 3)(x + 4)}$ remains

Step4: Combine the terms with the common denominator

$\frac{x(x + 4) - 3(x - 3) + 7}{(x - 3)(x + 4)}$

Answer:

$\frac{x(x + 4) - 3(x - 3) + 7}{(x - 3)(x + 4)}$ (First option)