x/7=x/5+5/7

Question

This is similare problems I have to study for my exam plus linear equations.

Answer 1

Multiply both sides by 35, the LCD,

5x = 7x + 25

Solve for x,

x = -25/2 <==Answer

Answer 2

I'm assuming you want to solve for x. 

You want to get everything over a common denominator. In the case of 5 and 7, the lowest common denominator is 35.

To x/7 to have a denominator of 35, we have to multiply it by 5/5: (x/7)*(5/5) = 5x/35

Do the same with 5/7: (5/7)*(5/5) = 25/35

With x/5, to get the denominator to 35 we multiply by 7/7: (x/5)*(7/7) = 7x/35

Now we have: 5x/35 = 7x/35 + 25/35. Multiply both sides by 35 to eliminate all the denominators:
(5x/35 = 7x/35 + 25/35)*35 ==> 5x = 7x + 25

Solve for x by combining like terms. Subtract 7x from both sides: -2x = 25

Divide both sides by -2: x = -12.5