# 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?

• Why not cancel? The calculation shows that if $x$ is a solution of the equation, then $0=49$. But $0$ is not $49$, so there cannot be a solution. – André Nicolas May 24 '15 at 3:38

There is no solution for the equation, maybe cause the question is wrong. Look that,

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

is equals

$$10x-4-10x-15=30$$

i.e,

$$0=49,$$

this is absurd.

• The question is designed to test whether the student understands that a contradiction means that there is no solution. – N. F. Taussig May 24 '15 at 9:37