Question

20x-25/3b-4 / 4a^2x-5a^2/16-9b^2

Answer 1

O.K.

Answer 2

(20x-25)/(3b-4) / (4a^2x-5a^2)/(16-9b^)

Answer 3

Good job

Answer 4

So we have

\[\frac{20x - 25}{3b - 4} \div\ \frac{4a^2x - 5a^2}{16-9b^2}\]

Answer 5

Yes.

Answer 6

(5(4x-5)

Answer 7

Use the reciprocal property to re-write the expression as

\[\frac{20x - 25}{3b - 4} \times\ \frac{16-9b^2 }{4a^2x - 5a^2}\]

Answer 8

Without negative exponents ?

Answer 9

If there are no negative exponents in the original expression, then we shouldn't have to worry about them. Usually, the goal is to try to avoid them or get rid of them.

Answer 10

We don't seem to be dealing with any at the moment. It seems that here, the only thing we have to concentrate on is simplifying the expression.

Answer 11

It becomes (5(4x-5)/(3b-4) / (a^2(4x-5)/((4-3b)*(4+3b))

Answer 12

Then we rewrite it, like you said.

Answer 13

For convenience, let's re-write it as

\[\frac{(4 - 3b)(4 + 3b)}{(3b - 4)} \times \frac{5(4x - 5)}{a^2(4x - 5)}\]

Answer 14

Also, let us take out a negative in the denominator so that we can re-write it as:

\[\frac{(4 - 3b)(4 + 3b)}{-(4 - 3b)} \times \frac{5(4x - 5)}{a^2(4x - 5)}\]

Then:
\[-\frac{(4 - 3b)(4 + 3b)}{(4 - 3b)} \times \frac{5(4x - 5)}{a^2(4x - 5)}\]

This way it is easier to see what cancels:

\[-\frac{\cancel{(4 - 3b)}(4 + 3b)}{\cancel{(4 - 3b)}} \times \frac{5\cancel{(4x - 5)}}{a^2\cancel{(4x - 5)}}\]

Answer 15

Thank you.

Answer 16

And thus the result is obvious from here:

\[-\frac{5(4 + 3b)}{a^2}\]

Answer 17

You're welcome