Y/a - b = y/b - a, if a≠b

solve for y

y = ab if a≠b

Step-by-step explanation:

y/a - b = y/b - a

multiply each side by ab to clear the fractions

ab (y/a - b) = ab (y/b - a)

distribute

ab * y/a - ab*b = ab * y/b - ab * a

b*y - ab^2 = ay - a^2 b

subtract ay on each side

by - ay - ab^2 = ay-ay - a^2b

by - ay - ab^2 = -a^2b

add ab^2 to each side

by-ay - ab^2 + ab^2 = ab^2 - a^2b

by-ay = ab^2 - a^2b

factor out the y on the left, factor out an ab on the right

y (b-a) = ab (b-a)

divide by (b-a)

y (b-a) / (b-a) = ab (b-a) / (b-a) b-a ≠0 or b≠a

y = ab