SOLUTION: I really need the solution (5/y-3)

SOLUTION: I really need the solution (5/y-3) - (30 /y^2-9) = 1

Question 76095: I really need the solution

(5/y-3) - (30 /y^2-9) = 1
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!

.
The denominator is the difference of two squares. The rule that applies to
factoring the difference between two squares is:
.

.
Applying this rule to results in:
.

.
Substituting this into the equation changes the equation to:
.

.
You can get all the terms over the common denominator of . Multiply the
first term by which is the same as multiplying the first term by 1 because
the numerator of this multiplier is the same as the denominator. When you do this
multiplication the equation becomes:
.

.
Then multiply the 1 on the right side by . This multiplication
results in:

.
Now you can multiply the entire equation (both sides, all terms) by the common denominator
and after that multiplication you are left with only the numerators
of all the terms in the equation. The result is:
.

.
Multiply where called for and the equation becomes:
.

.
Subtract from both sides to get:
.

.
Rearrange terms in descending powers of y:
.

.
Combine the constants:
.

.
Multiply the entire equation (both sides and all terms) by -1 to get:
.

.
This factors to:
.

.
If either of the factors equals zero, then the equation is true because a multiplication
by zero on the left side, makes the entire left side equal to the zero on the right side.
Find the solutions for y by setting each of the factors equal to zero and solving for
y ...
.
y - 2 = 0 <---- add 2 to both sides
.
y = +2 <--- one answer for y
.
y - 3 = 0 <--- add 3 to both sides
.
y = +3 <--- the second answer for y
.
But the second answer [y = +3] is not permitted because this would cause a division by
zero in the second term of the original equation ... the denominator of the second term
is and it is equal to and if y is allowed to equal
+3 then one of the factors in the denominator is zero ... and division by zero is not
permitted.
.
So there you are ... the answer to the equation is y = +2.
.
Hope this helps you to understand the problem a little better.
RELATED QUESTIONS
Hello, I really need urgent help on solving these following conics equations from it's... (answered by MathLover1)

Can you please tell me if i got these correct? Im doing a practice test to study for my... (answered by Edwin McCravy,solver91311)

how do I graph this linear system and estimate the solution then check the solution... (answered by ewatrrr)

I need help finding the real solution to this equation. (y - 2/3)^2 =... (answered by Alan3354)

I need help finding the real solution to this equation. (y - 2/3)^2 =... (answered by mananth,MathTherapy)

i have two solution sets from two linear equations equation one: y=4(x)-1 The... (answered by RAY100,solver91311)

I really don't understand these problems and need help. State the location of the foci (answered by venugopalramana)

I Really Need Help! It's Friday and i have tons of homework! I need help with Find the... (answered by MathTherapy)

I need help in doing this. For which system(s)is (2,3)the solution? I know I have to... (answered by elima)