How do you simplify #\frac { 1- \frac { 4} { x ^ { 2} } } { \frac { 5} { x } + \frac { 10} { x ^ { 2} } }#?

Question

381 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-11-29T17:55:43

Please see the explanation.

Multiply by 1 in the form #x^2/x^2#

#(1 - 4/x^2)/(5/x + 10/x^2)x^2/x^2#

Multiply numerators and denominators:

#(x^2 - 4x^2/x^2)/(5x^2/x + 10x^2/x^2)#

The denominators are canceled by common factors in the numerators:

#(x^2 - 4)/(5x + 10)#

The numerator is the difference of two squares; we know how that factors:

#((x - 2)(x + 2))/(5x + 10)#

Remove a factor of 5 from the denominator:

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

The common factor #x + 2# cancels:

#(x - 2)/5#

Simple enough, I think.