# How do you simplify (6x^2)/(4x^2) - 54/36?

Apr 6, 2018

Just in case simplification gives you a problem I have shown every step. Also a trick to test for divisibility by 3

Answer is 0. Becomes undefined at $x = 0$

#### Explanation:

Write as:

$\left[\frac{6}{4} \times {x}^{2} / {x}^{2}\right] - \frac{54}{36}$

But ${x}^{2} / {x}^{2} = 1$ unless $x = 0$. Dividing by 0 is not allowed mathematically. This is called 'undefined'.

1 times anything does not change the value. So we can disregard the $\times 1$

Now we have:

$\frac{6}{4} - \frac{54}{36}$

Notice that all the numbers are even. If simplifying gives you a problem you can use this type of approach:

$\left[\frac{6 \div 2}{4 \div 2}\right] - \left[\frac{54 \div 2}{36 \div 2}\right]$

$\frac{3}{2} - \left[\frac{27}{18}\right]$

Notice that for 27 we have $2 + 7 = 9$ which is divisible by 3 so 27 is also divisible by 3

Notice that for 18 we have the same thing: $1 + 8 = 9$

So we can divide both top and bottom by 3

$\frac{3}{2} - \left[\frac{27 \div 3}{18 \div 3}\right]$

$\frac{3}{2} - \left[\frac{9}{6}\right]$

$\frac{3}{2} - \left[\frac{9 \div 3}{6 \div 3}\right]$

$\frac{3}{2} - \frac{3}{2} = 0$