1Change into lowest terms: \( \frac{xy}{x^2y} \)
2Change into lowest terms: \( \frac{x-y}{x^2-y^2} \)
3Change into lowest terms: \( \frac{a+3}{a^2+5a+6} \)
4Change into lowest terms: \( \frac{a-2}{a^2-6a+8} \)
5Change into lowest terms: \( \frac{a-6}{a^2-8a+12} \)
6Change into lowest terms: \( \frac{a+2}{a^2-4a-12} \)
7Simplify: \( \frac{3}{5} + \frac{1}{5} \)
8Simplify: \( \frac{2}{3} + \frac{1}{5} \)
9Simplify: \( \frac{1}{4} + \frac{1}{6} \)
10Simplify: \( \frac{a}{b} + \frac{2a}{b} \)
11Simplify: \( \frac{3a}{b} - \frac{ab}{a} \)
12Simplify: \( \frac{3}{xy} + \frac{2a}{xy^2} \)
13Change into the simplest form: \( \frac{x^2-5x}{x^2-25} \)
14Change into the simplest form: \( \frac{a^2-b^2}{(a+b)^2} \)
15Change into the simplest form: \( \frac{x^2-5x+6}{x^2-7x+12} \)
16Simplify: \( \frac{a}{a-b} + \frac{b}{b-a} \)
17Simplify: \( \frac{1}{b-c} - \frac{b+c}{b^2-c^2} \)
18Simplify: \( \frac{1}{m-n} + \frac{1}{m+n} \)
19Simplify: \( \frac{m+n}{m-n} + \frac{m-n}{m+n} \)
20Simplify: \( \frac{1}{m+n} + \frac{n}{m^2-n^2} \)
21Simplify: \( \frac{3}{x^2-4} + \frac{1}{(x-2)^2} \)
22Simplify: \( \frac{a^3+b^3}{a^2-ab+b^2} + \frac{a^3-b^3}{a^2+ab+b^2} \)
23Simplify: \( \frac{4x^2+25y^2}{4x^2-25y^2} - \frac{2x-5y}{2x+5y} \)
24Simplify: \( \frac{4x^3}{x^4+a^4} - \frac{8x^7}{x^8-a^8} \)
25Simplify: \( \frac{x}{x-y} - \frac{x}{x+y} + \frac{2xy}{x^2+y^2} \)
26Simplify: \( \frac{3}{a+3} + \frac{4}{a-3} + \frac{9a}{2(9-a^2)} \)
27Simplify: \( \frac{1}{x+2y} - \frac{1}{x-2y} + \frac{2x}{4y^2-x^2} \)
28Simplify: \( \frac{a}{(a-b)(a-c)} + \frac{b}{(b-a)(b-c)} + \frac{c}{(c-b)(c-a)} \)
29Simplify: \( \frac{y-z}{x^2-(y-z)^2} + \frac{z-x}{y^2-(z-x)^2} + \frac{x-y}{z^2-(x-y)^2} \)
30Simplify: \( \frac{x^2-(a-b)^2}{(x+b)^2-a^2} + \frac{a^2-(x-b)^2}{(x+a)^2-b^2} + \frac{b^2-(x-a)^2}{(a+b)^2-x^2} \)
31Simplify: \( \frac{1}{p^2+7p+12} + \frac{2}{p^2+5p+6} - \frac{3}{p^2+6p+8} \)
32Simplify: \( \frac{x+3}{x^2+3x+9} + \frac{x-3}{x^2-3x+9} - \frac{54}{x^4+9x^2+81} \)
33Simplify: \( \frac{1}{x^2-5x+6} + \frac{2}{4x-x^2-3} - \frac{3}{x^2-3x+2} \)
34Simplify: \( \frac{b+2}{1+b+b^2} - \frac{b-2}{1-b+b^2} - \frac{2b^2}{1+b^2+b^4} \)
35Simplify: \( \frac{1}{1-b+b^2} - \frac{1}{1+b+b^2} - \frac{2b}{1-b^2+b^4} \)
36Simplify: \( \frac{a+c}{a^2+ac+c^2} + \frac{a-c}{a^2-ac+c^2} + \frac{2c^3}{a^4+a^2c^2+c^4} \)
37Simplify: \( \frac{1}{4(1-\sqrt{x})} - \frac{1}{4(1+\sqrt{x})} + \frac{2\sqrt{x}}{4(1-x)} \)
38Simplify: \( \frac{1}{8(1-\sqrt{x})} - \frac{1}{8(1+\sqrt{x})} + \frac{2\sqrt{x}}{8(1-x)} \)
39Simplify: \( \frac{1}{(a+1)^2} + \frac{1}{(a-1)^2} - \frac{2}{a^2-1} \)
40If \( \frac{a}{2x+1} + \frac{1}{x+2} = \frac{4x+5}{2x^2+5x+2} \), what is the value of \( a \)?
41If \( \frac{a}{2x-3} + \frac{b}{3x+4} = \frac{x+7}{6x^2-x-12} \), find the values of \( a \) and \( b \).
42Why is it wrong to cancel the \( x \) in \( \frac{x+y}{x} \) and write the answer as \( y \)?
43Simplify: \( \frac{2}{x-2} + \frac{3}{2-x} \)
44Why is the LCM method better than multiplying across for \( \frac{1}{a-b} - \frac{b}{a^2-b^2} \)?