Question

How do you evaluate `\frac { 2} { x } - \frac { 5} { 2x + 1}`?

Answer 1

`(2-x)/(2x^2+x)`

Explanation:

`(2)/(x) - (5)/(2x+1)`

`x` and `2x + 1` have no common factors.

to find a common denominator, both denominators must be multiplied together.

this gives:

`(2(2x+1))/(x(2x+1)) - (5x)/((2x+1)x)`

after expanding brackets:

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

`4x+2 - 5x = -x + 2`, or `2-x`

so the final fraction is:

`(2-x)/(2x^2+x)`

Answer 2

`2/x - 5/(2x+1)`
= `(4x+2)/(2x^2+x) - (5x)/(2x^2+x)`
= `(4x+2-5x)/(2x^2+x)`
= `(2-x)/(2x^2+x)`
= `-(x-2)/(x(2x+1))`

Explanation:

1. Multiply the numerator and the denominator of `2/x` by 2x+1 and `5/(2x+1)` by x
2. Subtract the numerators of each fraction but keep the denominator `2x^2+x`