Question

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

Answer 1

Explanation:

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

`(a)/(b) + (c)/(d) = (ad + cb)/(bd)`

So, to apply this to the given question:

`(x+3)/(x-6) +(1)/(x-2)`

=
`((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

=
`([(x*x) + (x*-2)+(3*x)+(3*-2)]+(x-6))/((x-6)(x-2))`

• Simplify.

=
`([x^2 -2x+3x-6]+(x-6))/((x-6)(x-2))`

• Remove parentheses.

=
`(x^2 -2x+3x-6+x-6)/((x-6)(x-2))`

• Simplify again.

=
`(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.

=
`(x(x+2))/((x-6)(x-2))`

Answer:

A)
`(x(x+2))/((x-6)(x-2))`