How do you subtract #\frac { 8- v } { v - 6} - \frac { 7v - 9} { 6- v }#?

1 Answer
smendyka
Dec 29, 2016

#(6v - 1)/(v - 6)#

Explanation:

First, in order to get both fractions over a common denominator multiple the second fraction by #color(red)((-1)/(-1))# which is the same as multiplying by #1# and therefore does not change the value of the fraction:

#(8 - v)/(v - 6) - (color(red)((-1)/(-1)) xx (7v - 9)/(6 - v))#

#(8 - v)/(v - 6) - color(red)((-1) xx (7v - 9))/(color(red)((-1)) xx (6 - v))#

#(8 - v)/(v - 6) - (-7v + 9)/(-6 + v)#

#(8 - v)/(v - 6) - (-7v + 9)/(v - 6)#

We can now combine the numerators over a common denominator being careful to manage the signs for the terms in the second fraction correctly:

#((8 - v) - (-7v + 9))/(v - 6)#

#(8 - v +7v - 9)/(v - 6)#

Next, we can group like terms in the numerator:

#(7v - v + 8 - 9)/(v - 6)#

#(6v - 1)/(v - 6)#

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