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.
