Question

Solve for y, z, x or t:

Answer 1

Problem 1

y + (y/a) = b

a*( y + (y/a) ) = a*b ... multiply both sides by 'a'

ay + a(y/a) = ab ... distribute

ay + y = ab

(a+1)y = ab .... factor

y(a+1) = ab

y = ab/(a+1) ... divide both sides by (a+1)

Answer: y = ab/(a+1)

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Problem 2

z - a = z/b

b(z - a) = b(z/b) .... multiply both sides by b

b(z - a) = z

bz - ab = z ... distribute

bz - ab+ab = z+ab ... add ab to both sides

bz = z+ab

bz-z = z+ab-z ... subtract z from both sides

bz-z = ab

z(b-1) = ab .... factor

z = ab/(b-1) .... divide both sides by (b-1)

Answer: z = ab/(b-1)

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Notes:

To clear out the fractions, I multiplied both sides by the denominator value.

The restriction that 'a' cannot equal -1, back in problem 1, is to avoid having the denominator (a+1) be equal to zero. We cannot divide by zero. A similar situation happens with problem 2 as well.