How do you simplify #\frac { 2- 2y ^ { 2} } { y ^ { 2} - 7y + 6}#?

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Answer 1 · 2017-09-26T18:13:17

See a solution process below:

First, factor the numerator and denominator as:

#(2(1 - y^2))/((y - 6)(y - 1)) =>#

#(2(1 + y)(1 - y))/((y - 6)(y - 1)) =>#

#(2(1 + y)[-1(y - 1)])/((y - 6)(y - 1)) =>#

#(-2(1 + y)(y - 1))/((y - 6)(y - 1))#

Now, cancel common terms in the numerator and denominator:

#(-2(1 + y)color(red)(cancel(color(black)((y - 1)))))/((y - 6)color(red)(cancel(color(black)((y - 1))))) =>#

#(-2(1 + y))/(y - 6)# or #(-2 - 2y)/(y - 6)#