Question

Drag each tile to the correct box. Not all tiles will be used. Consider the expression below. Place the steps required to determine the sum of the two expressions in the correct order.

Answer 1

Answer:

$\frac{3x+6}{x^{2}-x-6 } +\frac{2x}{x^{2} +x-12}=\frac{5x+12}{x^{2} +x-12}$

Step-by-step explanation:

The given expression is

$\frac{3x+6}{x^{2}-x-6 } +\frac{2x}{x^{2} +x-12}$

First, we need to factor each part of the expression

$\frac{3(x+2)}{(x+2)(x-3)} +\frac{2x}{(x-3)(x+4)}$

Remember that quadractic expression are factored in two binomial factors. The first quadratic expression factors are about two numbers which product is 6 and which difference is one. The second quadratic expression is about two numbers which product is 12 and which difference is 1.

Now, we simplify equal expression at each fraction.

$\frac{3}{(x-3)} +\frac{2x}{(x-3)(x+4)}$

Then, we use the least common factor about the denominators to sum those fractions. In this case, the least common factor is $(x-3)(x+4)$, because those are the factors present in the denominators.

Now, we divide each fraction by the least common factor, and then multiply the numeratos by its result.

$\frac{3(x+4)+2x}{(x-3)(x+4)}$

Finally, we multiply all products and sum like terms.

$\frac{3x+12+2x}{x^{2} +4x-3x-12}=\frac{5x+12}{x^{2} +x-12}$

Therefore, the sum of the initial expression is equal to

$\frac{5x+12}{x^{2} +x-12}$