# How do you solve #\frac { 6y } { 2y + 6} + \frac { y + 18} { 3y + 9} = \frac { 7y + 17} { y + 3}#?

##### 1 Answer

#### Answer:

No real solution. Read the explanation carefully.

#### Explanation:

We can rewrite it as:-

Cross multiply;

Taking

**BUT** there is a catch.

We might think that

We find that terms in the denominator become **zero.**

That means the expressions **undefined ** at **zero** is not defined. Hence we cannot say for sure whether the **left-hand-side** equals the **right-hand-side** or not. So **not a solution** to this equation.

**Where did we go wrong?**

Remember the step where we cross multiplied **non-zero**. Therefore cross multiplication in that step is only valid if **not a solution** and even if it turns out to be a solution after solving the subsequent equations, **we are going to neglect it**.

Just to be sure, I checked on wolfram.