Finding the $\dfrac{a}{b}$ values in quadratic equations

Question

I'm not very good at math so please bear with me my child gets the whole part of the equation except the beginning when you're supposed to multiply and add the two numbers and get the same two digits (I hope I making sense ) is there a trick to do this quickly? If anyone has any suggestions or help I really appreciate it .

Answer 1

Hint -

You can search online for tutorials on quadratic equations. Some of these explain things from basic. Also you are able to learn different methods like middle term splitting, discriminate, completing the square etc.

Answer 2

Do you mean as follows? Let $x$ and $y$ be two numbers such that $xy = x+y$. Find $x$ and $y$.

If so, you can convert the equation as follows: $$xy = x+y$$ $$ \implies xy - x = -y $$ $$\implies x(y-1) = -y $$ $$\implies x = \frac{y}{y-1}. $$ Hence, if you choose $y=2$, then $x = 2$ is an integer solution. Otherwise, you get fractions. For instance, if $y=5$ then $x = 5/4.$