How do you simplify #\frac { 3x ^ { 2} + 2x - 1} { 3x ^ { 2} + x - 2}#?
1 Answer
Jul 16, 2018
Explanation:
#"to simplify factor the numerator/denominator and cancel"#
#"common factors"#
#color(blue)"Numerator"#
#"the factors of the product "3xx-1=-3#
#"which sum to "+2" are "+3" and "-1#
#3x^2+3x-x-1larrcolor(blue)"factor by grouping"#
#=3x(x+1)-1(x+1)#
#=(x+1)(3x-1)#
#color(blue)"Denominator"#
#"the factors of the product "3xx-2=-6#
#"which sum to "+1" are "+3" and "-2#
#3x^2+3x-2x-2#
#=3x(x+1)-2(x+1)#
#=(x+1)(3x-2)#
#(3x^2+2x-1)/(3x^2+x-2)#
#=(cancel((x+1))(3x-1))/(cancel((x+1))(3x-2))=(3x-1)/(3x-2)#
#"with restriction "x!=2/3#
