How can you find $P(\frac{X}{Y-X}<0)$ if $X\sim Geometric(p)$ and $Y\sim Bernoulli(p)$

Let the independent random variables $X\sim Geometric(p)$ and $Y\sim Bernoulli(p)$, I want to prove that $P({\displaystyle \frac{X}{Y-X}}<0)=(p-1{)}^{2}(p+1)$

Do I need the joint probability mass function for this or should it be proven in some other way?

Let the independent random variables $X\sim Geometric(p)$ and $Y\sim Bernoulli(p)$, I want to prove that $P({\displaystyle \frac{X}{Y-X}}<0)=(p-1{)}^{2}(p+1)$

Do I need the joint probability mass function for this or should it be proven in some other way?