Answer:
[tex]\large\boxed{\dfrac{8x-17}{4x^2-36}}[/tex]
Step-by-step explanation:
[tex]\dfrac{7}{4x^2-36}+\dfrac{4}{2x+6}\\\\=\dfrac{7}{2^2x^2-6^2}+\dfrac{4}{2x+6}\\\\=\dfrac{7}{(2x)^2-6^2}+\dfrac{4}{2x+6}\qquad\text{use}\ (a+b)(a-b)=a^2-b^2\\\\=\dfrac{7}{(2x-6)(2x+6)}+\dfrac{4}{2x+6}\\\\\text{We must have the same denominator.}\\\\\text{LCD is}\ (2x-6)(2x+6)[/tex]
[tex]=\dfrac{7}{(2x-6)(2x+6)}+\dfrac{4(2x-6)}{(2x+6)(2x-6)}\\\\=\dfrac{7+4(2x-6)}{4x^2-36}\qquad\text{use the distributive property}\\\\=\dfrac{7+(4)(2x)+(4)(-6)}{4x^2-36}\\\\=\dfrac{7+8x-24}{4x^2-36}\\\\=\dfrac{8x+(7-24)}{4x^2-36}\\\\=\dfrac{8x-17}{4x^2-36}[/tex]
