Algebraic Fractions

Question

Simplify the following expression:



Answer 1

x / [y(x-y)] - y / [x(x-y)] LCD = xy(x-y)

= x² / [xy(x-y)] - y² / [xy(x-y)] = (x² - y²) / [xy(x - y)]

So, we have (x² - y²) / [xy(x-y)] ÷ (x² - y²) / (8xy)

= (x² - y²) / [xy(x-y)] · (8xy) / (x² - y²) = 8xy / [xy(x-y)] = 8 / (x-y)

Answer 2

Answer 3

We have to deal with what's inside the parentheses first. We have to make the denominators the same.

So the first step is to factor the denominators (factor out a y in the denominator of the first fraction, then factor out an x in the denominator in the second fraction):

[x/ y(x-y) ] - [y/x(x-y)].

Then multiply the numerator and denominator of the first fraction by x and multiply the numerator and denominator of the second fraction by y.

So we get: [x•x/xy(x-y)] - [y•y/ xy(x-y)] =

[x²/xy(x-y)]-[y²/xy(x-y)]= (x²-y²)/xy(x-y)

Now divide it by (x²-y²)/8xy

So we have (x²-y²)/xy(x-y) ÷ (x²-y²)/8xy

[(X²-y²)/xy(x-y)]×[8xy/ (x²-y²)] = 8/(x-y)

Answer 4

See the videa.

Answer 5

= 8/(x-y)

combine fractions

cancel factors

and surprise simplifications