Question

Solve the equations and check your solutions. If there is no solution, say so ( I have the answer which is y=-1 I just to know the step by step please. thanks in advance)
2/3+5/(y-4)=(y+6)/(3y-12)

Answer 1

\[\frac{2}{3}+\frac{5}{(y-4)}=\frac{(y+6)}{(3y-12)}\]
rewrite as

\[\frac{2}{3}+\frac{5}{(y-4)}=\frac{(y+6)}{3(y-4}\]

multiply both side of the equation by \[3(y-4)\] in order to "clear" the fractions

Answer 2

with the result

\[2(y-4)+3(5)=y+6\]

Answer 3

multiply and combine like terms with the result

\[2y+7=y+6\]
then finally isolating y we get
\[y= -1\]

Answer 4

no do not do it the hard way. there is no need to solve a quadratic equation here and in any case 4 is not a solution because you cannot replace y by 4 in the original expression

Answer 5

exactly

@Toriqur

when you combine fractions the way you have, you introduce extra factors into the equation.

In this case an extra factor of y-4

the least common denominator for the entire equation is 3(y-4)

Answer 6

ebbflo (nice) has it

Answer 7

satellite73: thanks for chiming in, this thread is more or less dead but its good to have good information none the less.

I have witnessed teachers instructing their students to combine fractions in exactly that manner because(i am guessing) it works out fine in the end when adding numerical fractions.

Answer 8

math teachers generally suck. if i see another question asking to "simplify" i am going to chuck a fit