How do you divide #\frac { 2x - 3} { x ^ { 2} - 16} \div \frac { 8x - 12} { 4- x }#?

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Answer 1 · 2017-08-29T13:03:51

#-1/(4(x+4)#

#(1) " "#Change the sum to a multiplication by inverting the second fraction .

#(2x-3)/(x^2-16)-:(8x-12)/((4-x)#

#=(2x-3)/(x^2-16)xx(4-x)/(8x-12)#

#(2)" "#Now factorise where possible

#=(2x-3)/((x-4)(x+4))xx(-(x-4))/(4(2x-3))#

#(3)" "#Cancel where possible

#=cancel(color(red)((2x-3)))/(cancel(color(blue)((x-4)))(x+4))xx(-cancel(color(blue)((x-4))))/(4cancel(color(red)((2x-3))))#

#=-1/(4(x+4)#