Question

Please help!! The question is the image below VVV Answers are also images after the picture.

Answer 1

Step-by-step explanation:

When adding two fractions with different bases (bottom numbers), we can use this function:

$\frac{a}{b} + \frac{c}{d} = \frac{ad + cb}{bd}$

So, to apply this to the given question:

$\frac{x+3}{x-6} +\frac{1}{x-2}$

= $\frac{(x+3)(x-2)+(1)(x-6)}{(x-6)(x-2)}$

From the given answers, we see we don't need to simplify the resulting base number, which makes things a lot easier.

• Multiply top using: (a + b)(c + d) = ac + ad + bc + bd

= $\frac{[(x*x) + (x*-2)+(3*x)+(3*-2)]+(x-6)}{(x-6)(x-2)}$

• Simplify.

= $\frac{[x^2 -2x+3x-6]+(x-6)}{(x-6)(x-2)}$

• Remove parentheses.

= $\frac{x^2 -2x+3x-6+x-6}{(x-6)(x-2)}$

• Simplify again.

= $\frac{x^2 +2x-12}{(x-6)(x-2)}$

Now if we wanna be a little smart, we can see that from here, the only answer that has x^2 and something else, is A. But, just for show, lets factor.

• Factor.

= $\frac{x(x+2)}{(x-6)(x-2)}$

Answer:

A) $\frac{x(x+2)}{(x-6)(x-2)}$