How do you evaluate #\frac { y - 4} { 7y + 63} - \frac { y + 5} { 9y + 81}#?

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Answer 1 · 2017-12-04T12:08:32

See a solution process below:

First, rewrite the denominator of each fraction as:

#(y - 4)/(7(y + 9)) - (y - 5)/(9(y + 9))#

Next, multiply each fraction by the appropriate form of 1 to put each fraction over a common denominator:

#(9/9 xx (y - 4)/(7(y + 9))) - (7/7 xx (y - 5)/(9(y + 9))) =>#

#(9(y - 4))/(9 * 7(y + 9)) - (7(y - 5))/(7 * 9(y + 9)) =>#

#((9 * y) - (9 * 4))/(63(y + 9)) - ((7 * y) - (7 * 5))/(63(y + 9)) =>#

#(9y - 36)/(63(y + 9)) - (7y - 35)/(63(y + 9))#

Now, we can subtract the numerators over their common denominators. Remembering to be careful to manage the signs of the individual terms correctly:

#((9y - 36) - (7y - 35))/(63(y + 9)) =>#

#(9y - 36 - 7y + 35)/(63(y + 9)) =>#

#(9y - 7y - 36 + 35)/(63(y + 9)) =>#

#((9 - 7)y + (-36 + 35))/(63(y + 9)) =>#

#(2y + (-1))/(63(y + 9)) =>#

#(2y - 1)/(63(y + 9))#