# Thread: Where do I start

1. ## Where do I start

If r is rational(r does not equal 0) and x is irrational, prove that r + x and rx irrational.

2. Originally Posted by Nichelle14
If r is rational(r does not equal 0) and x is irrational, prove that r + x and rx irrational.
Assume that,
$r+x$ is rational.
Thus,
$r+x=\frac{p}{q}$
Then,
$x=\frac{p}{q}-r$
But, $r$ is rational,
Thus,
$x$ must be rational.
----
Assume that,
$rx$ is rational.
Thus,
$rx=\frac{p}{q}$
Now, $r\not = 0$ thus,
$x=\frac{p}{rq}$
Thus, $x$ is rational.