# How do you find the LCD of (2-y^2)/(y^2-49 ), (y-4)/(y+7)?

Apr 24, 2017

See the solution process below:

#### Explanation:

The denominator for the fraction on the left is a special form of the quadratic:

$\left(a + b\right) \left(a - b\right) = \left({a}^{2} - {b}^{2}\right)$

If we let:

${a}^{2} = {y}^{2}$ then $\sqrt{{a}^{2}} = \sqrt{{y}^{2}}$ and $a = y$

${b}^{2} = 49$ then $\sqrt{{b}^{2}} = \sqrt{49}$ and $b = 7$

Therefore:

${y}^{2} - 49 = \left(y + 7\right) \left(y - 7\right)$

So, the lowest common denominator is:

$\textcolor{red}{{y}^{2} - 49}$

And to put the fraction on the right over the common denominator we need to multiply it by the appropriate form of $1$, which for this problem is $\frac{y - 7}{y - 7}$