Simplify fully the expression ( 7x^2 + 14x ) / ( 2x + 4 )

The first thing we try to do is factorise the numerator and denominator. Let's start with the numerator. We can take a 7 out of the bracket to leave us with 7( x² + 2x ) on the numerator. But we're not done! We can also take out an x to give us 7x( x + 2 ). We now try to factorise the denominator. The only thing we can factorise is a 2 so we're left with 2( x + 2 ).Altogether we now have 7x( x + 2 ) / 2( x + 2 ). We can see that both the numerator and denominator have a common factor of ( x + 2 ) and so they cancel. This gives us our final answer of 7x / 2.