Question

Perform the indicated operation 5/2x+3y divided by 10/4x^2-9y^2

Answer 1

The answer is (2x-3y) / 2

Explanation:

See the attached figure for solution

Answer 2

`(2x-3y)/(2)`

Explanation:

Dividing by a fraction means multiplying by the reciprocal. So we can write the problem as:

`(5)/(2x+3y)*(4x^2-9y^2)/(10)`

We can simplify
`4x^2-9y^2` into
`(2x+3y)(2x-3y)` by using the formula
`a^2-b^2=(a+b)(a-b)`

Now we can write:

`(5)/(2x+3y)*((2x-3y)(2x+3y))/(10)`

We can cancel out (2x+3y) and also reduce "5" and 10". Thus we have:

`(5)/(2x+3y)*((2x-3y)(2x+3y))/(10)\\=(1)/(1)*((2x-3y))/(2)\\=(2x-3y)/(2)`

This is the simplified form.