How do you simplify #\frac { 11y } { 6y + 1} - \frac { 5y - 1} { 6y + 1}#?

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Answer 1 · 2017-10-14T18:02:29

See a solution process below:

Because the denominator of the two fractions are the same we can subtract the numerators over the common denominator:

#(11y)/(6y + 1) - (5y - 1)/(6y + 1) =>#

#(11y - (5y - 1))/(6y + 1) =>#

#(11y - 5y - (-1))/(6y + 1) =>#

#(11y - 5y + 1)/(6y + 1) =>#

#((11 - 5)y + 1)/(6y + 1) =>#

#(6y + 1)/(6y + 1) =>#

#1#

However because we cannot divide by #0# we need to make sure the denominator is not equal to 0 in the original expression:

#6y + 1 = 0#

#6y + 1 - color(red)(1) = 0 - color(red)(1)#

#6y + 0 = -1#

#6y = -1#

#(6y)/color(red)(6) = -1/color(red)(6)#

#(color(red)(cancel(color(black)(6)))y)/cancel(color(red)(6)) = -1/6#

#y = -1/6#

Therefore: #(11y)/(6y + 1) - (5y - 1)/(6y + 1)# is #1# Where #y != -1/6#