SOLUTION: Solve (-3)/(y-4)=(1)/(y+4) (w-3)/(w+2)=(6-w)/(w-12) Please I need help with this! Thank you!

Question 825739: Solve
(-3)/(y-4)=(1)/(y+4)

(w-3)/(w+2)=(6-w)/(w-12)

Please I need help with this! Thank you!
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

Solving equations with fractions is harder than solving equations without fractions. So we will make the problem easier if we eliminate the fractions as soon as possible.

Fractions in an equation can be eliminated by...

Find the lowest common denominator (LCD) of all the fractions (on both sides of the equation).
Multiply both sides of the equation by the LCD.

Since the two denominators, (y-4) and (y+4), have no common factors the LCD is simply the product of the two denominators: (y-4)(y+4). So we will multiply both sides by (y-4)(y+4):

As we multiply, each denominator will cancel with some part of (y-4)(y+4):

leaving:

which simplifies to:

Now we can solve for y. Adding 3y to each side:

Adding 4 to each side:

Dividing both sides by 4:

Last we check. This is not optional! When both sides of an equation are multiplied by something that might be zero, like (y-4)(y+4), then a check is required. One must make sure that the solution does not make a factor of (y-4)(y+4) equal to zero. A quick visual check should tell us that if y = -2 (our solution) then neither (y-4) nor (y+4) will be a zero. So our solution checks!

I'll leave the second problem up to you to finish. I will just say that the denominators, (w+2) and (w-12), have no common factors between them. So, like the first problem, the LCD is simply their product: (w+2)(w-12)

P.S. This equation has rational expressions. It is not a rational function. It should be posted in the "polynomials, rational expressions ..." category.
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