how to solve for x?

Question

x/a + x/b =a + b

 

thank you!!

Answer 1

 

x/a + x/b = a+b

 

What you do is put the left hand side over a common denominator:

(b/b)*(x/a) + (a/a)*x/b = a+b   

bx/ab + ax/ab = a+b

(bx+ax)/ab = a+b

Factor out x:

x(a+b)/(ab) = a+b

Divide both sides by a+b

x/(ab) = 1

Multiply both sides by ab:

x = ab   (done)

 

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Check:   ab/a + ab/b = b+a = a+b  (ok)