Answer:
Step-by-step explanation:
Given the expression [tex]\frac{x}{x^{2}-2x-15 } - \frac{4}{x^{2} + 2x - 35 }[/tex], the dfference is expressed as follows;
Step1: First we need to factorize the denominator of each function.
[tex]\frac{x}{x^{2}-2x-15 } - \frac{4}{x^{2} + 2x - 35 }\\= \frac{x}{x^{2}-5x+3x-15 } - \frac{4}{x^{2} + 7x-5x - 35 }\\= \frac{x}{x(x-5)+3(x-5) } - \frac{4}{x( x+ 7)x-5(x +7) }\\= \frac{x}{(x-5)(x+3) } - \frac{4}{(x-5)(x +7) }\\\\[/tex]
Step 2: We will find the LCM of the resulting expression
[tex]= \frac{x}{(x-5)(x+3) } - \frac{4}{(x-5)(x +7) }\\= \frac{x(x+7)-4(x+3)}{(x-5)(x+3)(x+7)} \\= \frac{x^{2}+7x-4x-12 }{(x-5)(x+3)(x+7)} \\= \frac{x^{2}+3x-12 }{(x-5)(x+3)(x+7)} \\[/tex]
The final expression gives the difference
