How do you divide #\frac { 6x ^ { 2} } { x ^ { 2} - 25} \div \frac { x ^ { 4} } { ( x - 5) ^ { 2} }#?

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Answer 1 · 2018-05-23T01:14:06

#(6(x-5))/(x^2(x+5))#

#\frac { 6x ^ { 2} } { x ^ { 2} - 25} \div \frac { x ^ { 4} } { ( x - 5) ^ { 2} }#

You take the inverse of either term and then multiply:

#(6x^2)/(x^2 - 25)*((x-5)^2)/x^4#

factor:

#(6x^2)/((x - 5)(x+5))*((x-5)(x-5))/x^4#

Divide off like terms (you can eliminate across the multiplication):

#(6)/((x+5))*((x-5))/x^2#

#(6(x-5))/(x^2(x+5))#

I would probably leave it there, you can distribute the terms but that is no simpler.