Question

Build up the denominator x/x-5, ?/x2-x-20

Answer 1

Is this what you mean?
For the fractions to be equivalent, what numerator do you need in the second fraction?

\(\dfrac{x}{x-5} = \dfrac{ ?}{x^2-x-20} \)

Answer 2

Yes

Answer 3

Start by factoring the right denominator.

Answer 4

Do you know how to factor \(x^2 - x - 20\) ?

Answer 5

Would it be x-20?

Answer 6

I'm so lost! Please help!

Answer 7

No.
You need two binomials that multiply to \(x^2 - x - 20\).
You need to find 2 numbers that multiply to -20 and add to -1.
Can you come up with such numbers?

Answer 8

-5 and 4

Answer 9

Is that it? What's next?

Answer 10

Great.
Now you place the numbers like this:

(x - 5)(x + 4)
That's how you factor it.

Answer 11

Now that we factored the right denominator, we have:

\(\dfrac{x}{x-5} = \dfrac{ ?}{(x-5)(x+4)}\)

Ok?

Answer 12

To make the fractions equal, you need to multiply the left fraction by (x + 4)/(x + 4)

\(\dfrac{x}{x-5} = \dfrac{ x(x + 4)}{(x-5)(x+4)}\)

Answer 13

So the answer is x/x-5

Answer 14

The answer is x(x + 4) which in what the right numerator needs to be for the fractions to be equivalent.