Fractions and Largest Common Multiple, Algebra, Numerator and Denominator Identical Numbers?

This is the question find x of equation:

$\frac{5x-2}{5}-\frac{2x+3}{2}=3$

I tried multiplying this all by 10, the LCM. It ended with:

$x-x=49.$

How do you solve this without cancelling the x out of the equation?

This is the question find x of equation:

$\frac{5x-2}{5}-\frac{2x+3}{2}=3$

I tried multiplying this all by 10, the LCM. It ended with:

$x-x=49.$

How do you solve this without cancelling the x out of the equation?