How do you combine #(x-10)/(x-8)-(x+10)/(8-x)#?

Question

1370 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-02-04T04:12:07

See the entire solution process below:

First, we need to put the fractions over common denominators. We can do this by multiplying the first fraction by the appropriate form of #1#:

#((-1)/-1 xx (x - 10)/(x - 8)) - (x + 10)/(8 - x) ->#

#((-1 xx (x - 10))/(-1 xx (x - 8))) - (x + 10)/(8 - x) ->#

#(-x + 10)/(-x + 8) - (x + 10)/(8 - x) ->#

#(-x + 10)/(8 - x) - (x + 10)/(8 - x)#

Now that there is a common denominator for each fraction we can subtract the numerators:

#(-x + 10 - x - 10)/(8 - x)#

#(-x - x + 10 - 10)/(8 - x)#

#(-2x + 0)/(8 - x)#

#(-2x)/(8 - x)#