Solve for w.

-4/w-8 = -2/w+1

-4[(w-8)(w+1)]/w-8 = -2[(w-8)(w+1)]/w+1 Multiply both sides by (w − 8)(w + 1)

-4(w+1) = -2(w-8) Simplify

-4w-4 = -2w+16 Apply the distributive property

-2w-4 = 16 Add 2w to both sides

-2w = 20 Add 4 to both sides

w = -10 Divide both sides by ^–2

Now check whether this is an extraneous solution. Plugging w = -10 into the first denominator, w-8 , yields -18 . Plugging w = -10  into the second denominator, w+1 , yields -9 .Since neither denominator is 0, which would be undefined, this is a valid solution.

The solution is w = -10

Solve for u.

8/u+3 = 3/u-2

8[(u+3)(u-2)]/u+3 = 3[(u+3)(u-2)]/u-2 Multiply both sides by (u + 3)(u − 2)

8(u-2) = 3(u+3) Simplify

8u-16 = 3u+9 Apply the distributive property

5u-16 = 9 Subtract 3u from both sides

5u = 25 Add 16 to both sides

u = 5 Divide both sides by 5

Now check whether this is an extraneous solution. Plugging u = 5 into the first denominator, u+3 , yields 8. Plugging u = 5 into the second denominator, u-2, yields 3  Since neither denominator is 0, which would be undefined, this is a valid solution.

The solution is u = 5

Solve for k.

k-8/6 = k-10/7

(k-8)(6 . 7) / 6 = (k-10)(6 .7)/7 Multiply both sides by 6 · 7

7(k-8) = 6(k-10) Simplify

7k-56 = 6k-60 Apply the distributive property

k-56 = -60 Subtract 6k from both sides

k = -4 Add 56 to both sides

Now check whether this is an extraneous solution. Since neither denominator is 0, which would be undefined, this is a valid solution.

The solution is k = -4