#"factorise the numerators/denominators of both fractions"#
#"and cancel any common factors"#
#•color(white)(x)x^2+2x-80#
#"factors that multiply to - 80 and sum to + 2"#
#"are + 10 and - 8"#
#rArrx^2+2x-80=(x+10)(x-8)#
#•color(white)(x)x^2-100color(blue)" is a difference of squares"#
#rArrx^2-100=(x-10)(x+10)#
#•color(white)(x)x^2-9x-10#
#"factors that multiply to - 10 and sum to - 9"#
#"are - 10 and +1"#
#rArrx^2-9x-10=(x-10)(x+1)#
#•color(white)(x)x^2-4x-32#
#"factors that multiply to - 32 and sum to - 4"#
#"are - 8 and +4"#
#rArrx^2-4x-32=(x-8)(x+4)#
#(x^2+2x-80)/(x^2-100)xx(x^2-9x-10)/(x^2-4x-32)#
#=(cancel((color(red)(x+10)))cancel((color(blue)(x-8))))/(cancel((color(magenta)(x-10)))cancel((color(red)(x+10))))xx(cancel((color(magenta)(x-10)))(x+1))/(cancel((color(blue)(x-8)))(x+4))#
#=(x+1)/(x+4)to(x!=-4)#
