Question

Perform the indicated operations

if

Answer 1

`(x^2 - 9)/(y^2 - 25) / (2x^2 - 6x)/(3y^2 - 15y) + (3 - 1.5y)/(y + 5) = (3(3y + 2x))/(2x(y+5))` If
`x \\e 0 \ \ or\ y \\e 0`

Explanation:

Given

`(x^2 - 9)/(y^2 - 25) / (2x^2 - 6x)/(3y^2 - 15y) + (3 - 1.5y)/(y + 5)`

Required

Solve

First, we change / to *

`(x^2 - 9)/(y^2 - 25) * (3y^2 - 15y)/(2x^2 - 6x) + (3 - 1.5y)/(y + 5)`

Apply difference of two squares

`((x- 3)(x+3))/((y - 5)(y+5)) * (3y^2 - 15y)/(2x^2 - 6x) + (3 - 1.5y)/(y + 5)`

Factorize:

`((x- 3)(x+3))/((y - 5)(y+5)) * (3y(y - 5))/(2x(x - 3)) + (3 - 1.5y)/(y + 5)`

x - 3 cancels out:

`((x+3))/((y - 5)(y+5)) * (3y(y - 5))/(2x) + (3 - 1.5y)/(y + 5)`

y - 5 cancels out

`(x+3)/(y+5) * (3y)/(2x) + (3 - 1.5y)/(y + 5)`

`(3y(x+3))/(2x(y+5)) + (3 - 1.5y)/(y + 5)`

Take L.C.M

`(3y(x+3) + 2x(3 - 1.5y))/(2x(y+5))`

Open brackets

`(3xy+9y + 6x - 3xy)/(2x(y+5))`

Collect Like Terms

`(3xy- 3xy+9y + 6x )/(2x(y+5))`

`(9y + 6x)/(2x(y+5))`

Factorize:

`(3(3y + 2x))/(2x(y+5))`

Hence:

`(x^2 - 9)/(y^2 - 25) / (2x^2 - 6x)/(3y^2 - 15y) + (3 - 1.5y)/(y + 5) = (3(3y + 2x))/(2x(y+5))` If
`x \\e 0 \ \ or\ y \\e 0`