For anybody who can't see the graphic, the exercises are as follows:
. . . . .Simplify:
. . . . .\(\displaystyle \large{1)\mbox{ }\frac{x^2\mbox{ }-\mbox{ }2xy\mbox{ }+\mbox{ }xy\mbox{ }-\mbox{ }2y^2}{3xy\mbox{ }+\mbox{ }3y^2\mbox{ }-\mbox{ }x^2\mbox{ }-\mbox{ }xy}}\)
. . . . .\(\displaystyle \large{2)\mbox{ }\frac{\frac{a}{a\mbox{ }+\mbox{ }b}\mbox{ }+\mbox{ }\frac{b}{a\mbox{ }-\mbox{ }b}}{\frac{b}{a\mbox{ }+\mbox{ }b}\mbox{ }-\mbox{ }\frac{a}{a\mbox{ }-\mbox{ }b}}}\)
. . . . .\(\displaystyle \large{3)\mbox{ }1\mbox{ }-\mbox{ }\frac{1}{1\mbox{ }+\mbox{ }\frac{1}{x\mbox{ }-\mbox{ }\frac{1}{x}}}}\)
To the poster:
1) Factor "by grouping", and cancel common factors, if any.
2) One method would be to multiply through, top and bottom, by the overall common denominator of (a + b)(a - b). Then simplify the result.
3) Work from the bottom up.
Eliz.