How do you subtract #\frac { x + y } { 5x - y } - \frac { 8x } { y - 5x }#?

1 Answer
smendyka
Jul 25, 2017

See a solution process below:

Explanation:

To subtract fractions they must be over a common denominator. We can make the second fraction have the same denominator by multiplying it by the appropriate form of #1# which will not change its value:

#(x + y)/(5x - y) - ((-1)/-1 xx (8x)/(y - 5x)) =>#

#(x + y)/(5x - y) - (-8x)/(-1(y - 5x)) =>#

#(x + y)/(5x - y) - (-8x)/(-1y - (-1 xx 5x)) =>#

#(x + y)/(5x - y) - (-8x)/(-1y - (-5x)) =>#

#(x + y)/(5x - y) - (-8x)/(-1y + 5x) =>#

#(x + y)/(5x - y) - (-8x)/(5x - 1y) =>#

#(x + y)/(5x - y) - (-8x)/(5x - y)#

With both fractions having the same denominator we can subtract the numerators over the common denominator:

#(x + y - (-8x))/(5x - y) =>#

#(x + y + 8x)/(5x - y) =>#

#(x + 8x + y)/(5x - y) =>#

#(1x + 8x + y)/(5x - y) =>#

#((1 + 8)x + y)/(5x - y) =>#

#(9x + y)/(5x - y)#

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