Help with alegbra fractions?

Question

3/z-3 + 5/z-1= 8/z-2

Answer 1

the LCD is (z - 1)(z - 2)(z - 3); therefore multiply by this value to clear the fraction

3(z - 1)(z - 2) + 5(z - 2)(z - 3) = 8(z - 1)(z - 3)

3(z^2 - 3z + 2) + 5(z^2 - 5z + 6) = 8(z^2 - 4z + 3)

3z^2 - 9z + 6 + 5z^2 - 25z + 30 = 8z^2 - 32z + 24

8z^2 - 34z + 36 = 8z^2 - 32z + 24

12 = 2z

z = 6

check: 3 / (6 - 3) + 5 / (6 - 1) = 3/3 + 5/5 = 1 + 1 = 2

8/(6 - 2) = 8 / 4 = 2 check!

Answer 2

Multiply both sides by LCD = (z-1)(z-2)(z-3),

3(z-1)(z-2) + 5(z-2)(z-3) = 8(z-1)(z-3)

Can you finish it now?

Answer 3

the LCD is (z - 1)(z - 2)(z - 3); therefore multiply by this value to clear the fraction