Question

a1" title=" \frac{2x}{x - 3} - \frac{4x}{x - 4} " alt=" \frac{2x}{x - 3} - \frac{4x}{x - 4} " align="absmiddle" class="latex-formula">

Answer 1

The first step for solving this expression is to write all numerators above the least common denominator. For this problem,, our least common denominator will be (x - 3) × (x - 4). 
$\frac{2xX(x-4)-4xX(x-3)}{(x-3)X(x-4)}$
Now we will distribute 2x through the first set of parenthesis.
$\frac{2 x^{2} -8x-4x X(x-3)}{(x-3)X(x-4)}$
Distribute -4x through the second set of parenthesis.
$\frac{2 x^{2} -8x-4 x^{2} +12x}{(x-3)X(x-4)}$
Multiply the two parentheses in the denominator of the fraction together.
$\frac{2 x^{2} -8x-4 x^{2} +12x}{ x^{2} -4x-3x+12}$
Collect the like terms with a variable of x² on the numerator (top) of the fraction.
$\frac{-2 x^{2} -8x+12x}{ x^{2} -4x-3x+12}$
Collect the terms on the numerator of the fraction with a variable of x. 
$\frac{-2 x^{2} +4x}{ x^{2} -4x-3x+12}$
Lastly,, collect the terms with an x variable on the denominator (bottom) of the fraction to get your final answer. 
$\frac{-2 x^{2} +4x}{ x^{2} -7x + 12}$
Let me know if you have any further questions.
:)