I'll show you how to do this two different ways. It is worth seeing both, because they are both useful. You can decide which is easier ;-)

I take the top expression (numerator) and turn it into a single fraction with denominator *x*.

`3+1/x=(3x+1)/x`

We do likewise with the bottom expression (denominator):

`5/x+4=(5+4x)/x`

So the question has become:

`(3+1/x)/(5/x+4)=((3x+1)/x)/((5+4x)/x)`

We think of the right side as a division of the top by the bottom:

`(3x+1)/x-:(5+4x)/x`

To divide by a fraction, you multiply by the reciprocal:

`(3x+1)/(x)xxx/(5+4x)=(3x+1)/(5+4x)`

The *x*'s cancelled out, and we have our final answer, which cannot be simplified any more.

I recognise that I have "/*x*" in both the numerator and denominator. So if I just multiply top and bottom by *x*, it will simplify everything by removing the fractions on top and bottom.

`(3+1/x)/(5/x+4)xxx/x`

I am really just multiplying by "1" and not changing the original value of the fraction - just changing its form.

So I multiply each element of the top by *x* and each element of the bottom by *x* and I get:

`(3+1/x)/(5/x+4)xxx/x=(3x+1)/(5+4x)`

I cannot simplify any further.

Get the Daily Math Tweet!

IntMath on Twitter