Question

I need help please and thank you

Answer 1

`\large\boxed{(8x-17)/(4x^2-36)}`

Explanation:

`(7)/(4x^2-36)+(4)/(2x+6)\\\\=(7)/(2^2x^2-6^2)+(4)/(2x+6)\\\\=(7)/((2x)^2-6^2)+(4)/(2x+6)\qquad\text{use}\ (a+b)(a-b)=a^2-b^2\\\\=(7)/((2x-6)(2x+6))+(4)/(2x+6)\\\\\text{We must have the same denominator.}\\\\\text{LCD is}\ (2x-6)(2x+6)`

`=(7)/((2x-6)(2x+6))+(4(2x-6))/((2x+6)(2x-6))\\\\=(7+4(2x-6))/(4x^2-36)\qquad\text{use the distributive property}\\\\=(7+(4)(2x)+(4)(-6))/(4x^2-36)\\\\=(7+8x-24)/(4x^2-36)\\\\=(8x+(7-24))/(4x^2-36)\\\\=(8x-17)/(4x^2-36)`