How do you write the rational expression #(2x^2+7x-30)/(2x^2-15x+25)# in lowest terms?

1 Answer
Jim G.
Jun 18, 2018

#(x+6)/(x-5)#

Explanation:

#"factor the numerator/denominator and cancel common"#
#"factors"#

#color(blue)"numerator"#

#"using the a-c method to factor"#

#"the factors of the product "2xx-30=-60#

#"which sum to + 7 are + 12 and - 5"#

#"split the middle term using these factors"#

#2x^2+12x-5x-30larrcolor(blue)"factor by grouping"#

#=color(red)(2x)(x+6)color(red)(-5)(x+6)#

#=(x+6)(2x-5)#

#color(blue)"denominator"#

#"the factors of the product "2xx25=50#

#"which sum to - 15 are - 10 and - 5"#

#2x^2-10x-5x+25#

#=2x(x-5)-5(x-5)#

#=(x-5)(2x-5)#

#rArr(2x^2+7x-30)/(2x^2-15x+25)#

#=((x+6)cancel((2x-5)))/((x-5)cancel((2x-5)))=(x+6)/(x-5)#

#"with restriction "x!=5#

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