How do you divide #\frac { 5x ^ { 2} + 11x + 2} { x ^ { 2} + 2x - 3} \div \frac { x ^ { 2} + 5x + 6} { 5x ^ { 2} - 6x + 1}#?

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Answer 1 · 2018-01-26T18:33:10

#(25x^2-1)/(x+3)^2#

#(5x^2+11x+2)/(x^2+2x-3) -: (x^2+5x+6)/(5x^2-6x+1)#

First, let's rewrite this. When we divide fractions, we are really just multiplying by the reciprocal:

#(5x^2+11x+2)/(x^2+2x-3) xx (5x^2-6x+1)/(x^2+5x+6)#

Now let's factor this and see if anything can be simplified:

#((x+2)(5x+1))/((x-1)(x+3)) xx ((5x-1)(x-1))/((x+2)(x+3))#

simplify

#((cancel(x+2))(5x+1))/((cancel(x-1))(x+3)) xx ((5x-1)(cancel(x-1)))/((cancel(x+2))(x+3))#

#((5x+1) xx (5x-1))/((x+3)(x+3))#

#(25x^2-1)/(x+3)^2#