How do you subtract #(3x+1)/(2x) - (x+1)/(x-3)#?

1 Answer
Apr 11, 2017

#(x^2-10x-3)/(2x(x-3))#

Explanation:

Before we can subtract the fractions we require them to have a #color(blue)"common denominator"#

To obtain this.

#"multiply numerator/denominator of " (3x+1)/(2x)" by " (x-3)#

#"multiply numerator/denominator of " (x+1)/(x-3)" by " 2x#

#rArr((3x+1)(color(red)(x-3)))/(2x(color(red)(x-3)))-(color(magenta)(2x)(x+1))/(color(magenta)(2x)(x-3))#

The fractions now have a common denominator so we can subtract the numerators while leaving the denominator.

#=((3x+1)(x-3)-2x(x+1))/(2x(x-3))#

distributing the numerator and simplifying gives.

#=(3x^2-8x-3-2x^2-2x)/(2x(x-3))#

#=(x^2-10x-3)/(2x(x-3))#