How do you divide and simplify #\frac { 4} { x + 5} \div \frac { 8x + 16} { x ^ { 2} + 7x + 10}#?

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Answer 1 · 2017-03-18T16:15:10

#1/2#

Observe that 2+5 =7 and that #2xx5=10# so we can write:

#4/(x+5)-:(8x+16)/(x^2+7x+10)" "->" "4/(x+5)-:(8x+16)/((x+2)(x+5))#

Factor out the 8 from #8x+16" giving "8(x+2)# so we can write:

#4/(x+5)-:(8(x+2))/((x+2)(x+5))#

Invert and multiply the divisor giving:

#4/(x+5)xx((x+2)(x+5))/(8(x+2))#

This is the same as

#4/8xx(x+5)/(x+5)xx(x+2)/(x+2)#

#1/2xx" "1" "xx" "1" "=" "1/2#