Question

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

Answer 1

See the solution process below:

Explanation:

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

`(a + b)(a - b) = (a^2 - b^2)`

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 = (y + 7)(y - 7)`

So, the lowest common denominator is:

`color(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 `(y - 7)/(y - 7)`