1. Factor the denominators as follow:
[tex]\begin{gathered} 4x-4=4(x-1) \\ \\ \\ x^2+5x-6 \\ =x^2+6x-x-6 \\ =x(x+6)-(x+6) \\ =(x-1)(x+6) \\ \\ \\ \\ \\ \frac{9x}{4(x-1)}+\frac{x^2-6x}{(x-1)(x+6)} \end{gathered}[/tex]2. Write the expresion with the less common denominator:
Multiply the first fraction by (x+6) (both parts, numerator and denominator):
[tex]\frac{9x}{4(x-1)}\cdot\frac{x+6}{x+6}=\frac{9x(x+6)}{4(x-1)(x+6)}[/tex]Multiply the second fraction by 4 (both parts, numerator and denominator):
[tex]\frac{x^2-6x}{(x-1)(x+6)}\cdot\frac{4}{4}=\frac{4(x^2-6x)}{4(x-1)(x+6)}[/tex]Rewrite the expression with the less common denominator:
[tex]\begin{gathered} \frac{9x(x+6)}{4(x-1)(x+6)}+\frac{4(x^2-6x)}{4(x-1)(x+6)} \\ \\ =\frac{9x(x+6)+4(x^2-6x)}{4(x-1)(x+6)} \end{gathered}[/tex]3. Remove parentheses and simplify:
[tex]\begin{gathered} \frac{9x^2^{}+54x+4x^2-24x}{(4x-4)(x+6)} \\ \\ =\frac{13x^2+30x}{4x^2+24x-4x-24} \\ \\ =\frac{13x^2+30x}{4x^2+20x-24} \end{gathered}[/tex]
