Answer:
[tex]\frac{x^2+19x-56}{4x^2-32x}[/tex]
Step-by-step explanation:
To add two fractions we need a common denominator. Just by looking at the two, there are no common factors. This means the denominator would be the product of the two: 4x(x-8). In order to obtain this, we multiply the first fraction by (x-8)/(x-8) - 1, and the second by 4x/4x - 1:
[tex]\frac{x+7}{4x} *\frac{x-8}{x-8} +\frac{5}{x-8}*\frac{4x}{4x}[/tex]
We can use the distributive property to simplify:
[tex]\frac{x^2-x-56}{4x(x-8)} +\frac{20x}{4x(x-8)}[/tex]
The sum of the two is:
[tex]\frac{x^2+19x-56}{4x^2-32x}[/tex]
