How do you evaluate \frac { 2} { x } - \frac { 5} { 2x + 1}2x52x+1?

2 Answers
Jan 23, 2018

(2-x)/(2x^2+x)2x2x2+x

Explanation:

(2)/(x) - (5)/(2x+1)2x52x+1

xx and 2x + 12x+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)2(2x+1)x(2x+1)5x(2x+1)x

after expanding brackets:

(4x+2)/(2x^2+x) - (5x)/(2x^2+x)4x+22x2+x5x2x2+x

4x+2 - 5x = -x + 24x+25x=x+2, or 2-x2x

so the final fraction is:

(2-x)/(2x^2+x)2x2x2+x

2/x - 5/(2x+1)2x52x+1
= (4x+2)/(2x^2+x) - (5x)/(2x^2+x)4x+22x2+x5x2x2+x
= (4x+2-5x)/(2x^2+x)4x+25x2x2+x
= (2-x)/(2x^2+x)2x2x2+x
= -(x-2)/(x(2x+1))x2x(2x+1)

Explanation:

  1. Multiply the numerator and the denominator of 2/x2x by 2x+1 and 5/(2x+1)52x+1 by x
  2. Subtract the numerators of each fraction but keep the denominator 2x^2+x2x2+x