Question

Perform the division. Assume no division by 0. Please help fast 30 points

Answer 1

Since (2x+5)(2x-5) = 4x^2-25,

then (4x^2-25)/(2x+5) = 2x-5

Answer 2

2x + 5

Explanation:

Given rational expression:

`(4x^2-25)/(2x+5)`

Factor the numerator

Rewrite the numerator as the difference of two squares:

`\implies 4x^2-25`

`\implies (2x)^2-(5)^2`

`\textsf{Apply\;the\;Difference\;of\:Two\;Squares\;formula}: \quad a^2-b^2=\left(a+b\right)\left(a-b\right)`

`\implies (2x)^2-(5)^2=(2x+5)(2x-5)`

Therefore:

`\implies (4x^2-25)/(2x+5)=((2x+5)(2x-5))/(2x-5)`

Cancel the common factor (2x - 5):

`\implies ((2x+5)(2x-5))/(2x-5)=2x+5`