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

2 Answers
Jan 23, 2018

(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)

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