How do you simplify #(2x-1)/((x-3)(x+2)) + (x-4)/(x-3)#?
2 Answers
Aug 2, 2018
Explanation:
#"We require the fractions to have common denominators"#
#"multiply the numerator/denominator of"#
#(x-4)/(x-3)" by "(x+2)#
#=(2x-1)/((x-3)(x+2))+((x-4)(x+2))/((x-3)(x+2))#
#=(2x-1)/((x-3)(x+2))+(x^2-2x-8)/((x-3)(x+2))#
#"add terms on numerators leaving the denominator"#
#=(x^2-9)/((x-3)(x+2))larrcolor(blue)"difference of squares"#
#=(cancel((x-3))(x+3))/(cancel((x-3))(x+2))larrcolor(blue)"cancel common factor"#
#=(x+3)/(x+2)#
#"with restriction "x!=3#
Aug 2, 2018