Algebra 2 problem help

Question

Suppose a and are positive real numbers

ab=(1/9)

a(b+1)=(7/9)

b(a+1)=18

What is (a+1)(b+1)?

Answer 1

ab=(1/9)

Using this equation, divide both sides by a

a(b+1)=(7/9)

a(b+1)/a=(7/9)/a Simplify

(b+1)=(7/9)/a

Using this equation, divide both sides by b

b(a+1)=18

b(a+1)/b=18/b Simplify

(a+1)=18/b

Now plug both of this into this equation provided.

(a+1)(b+1)

(18/b)((7/9)/a) Simplify the numerator

14/(ab)

Now there is ab in the denominator. We know ab=(1/9) so this can be plugged in

14/(1/9) Change division of the fraction to multiplication by the reciprocal

14(9/1) = 126