X+3x/4=7x/4

Question

X+3x/4=7x/4

Shouldn't I add the numerator straight across and the denominator straight across and look at it like this,

1x/1+3x/4= 4x/4=1x

 It appears the I have to add the numerator and the denominator  and place it over the old denominator but why?

Answer 1

No, to eliminate the denominators, you multiply both sides of the equation by the Least Common Denominator, LCD.

Here that number is 4

 

x + 3x/4 = 7x/4

4x + 3x = 7x

7x = 7x

 

This is an Identity. Any (that means "all") value of x solves. 

Answer 2

x+(3x/4)=(7x/4)

(x/1)+(3x/4)=(7x/4)

(4x/4)+(3x/4)=(7x/4)

(7x/4)=(7x/4)

this is an identity so there are infinitely many solutions