How do you simplify #\frac { 8x } { x ^ { 2} - 9x + 14} \div \frac { x ^ { 2} + 5x } { x ^ { 2} - 4} \div \frac { x + 2} { x - 7}#?

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Answer 1 · 2017-08-09T11:08:38

#8/(x+5#

First, we get rid of the division symbols by turning them into multiplication by getting the reciprocal of the fraction, giving us a new equation of

#(8x)/(x^2-9x+14)times(x^2-4)/(x^2+5x)times(x-7)/(x+2)#

We then factorise all the values we can to their simplest form, giving us

#(8x)/((x-7)(x-2))times((x-2)(x+2))/(x(x+5))times(x-7)/(x+2)#

We then get rid of common factors, simplifying the equation down to

#(8)/1times1/((x+5))times1/1#

Giving us the answer of

#8/(x+5#