Can someone explain how to get x by itself in the equation x over a plus x over b equals 1 I know there answer is ab over a plus b but i don't know why?

Answer 1

x/a + x/b = 1

Taking x as a common factor: x*(1/a + 1/b) = 1

Adding the fractional parts x*(b/ab + a/ab) = 1

or x*[(b + a)/ab] = 1

Multiply both sides by (a+b)/ab

x = (a+b)/ab

Another Approuch:-

x/a+x/b = 1

Multiply all terms by ab to eliminate the fractions:

bx+ax = ab

Factorise:

x(a+b) = ab

Divide both sides by (a+b):

x = ab/(a+b)