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

1 Answer
Apr 24, 2017

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)#