$\frac{a^{2} + 3ab}{a^{2}b + 3ab}$=$\frac{a(a + 3b)}{a(ab + 3b} = \frac{a + 3b}{ab + 3b}$

$\frac{x^{2} - x - 6}{x^{2} + x - 2} = \frac{\left( x + 2 \right)(x - 3)}{\left( x + 2 \right)(x - 1)} = \frac{x - 3}{x - 1}\ $

$\frac{2x^{3} - 2y^{3}}{5x^{2} - 5y^{2}} = \frac{2\left( x - y \right)(x^{2} + xy + y^{2}}{5\left( x - y \right)(x + y)} = \frac{2(x^{2} + xy + y^{2}}{5(x + y)}$

$\frac{3x^{2}}{2ab^{2}}$=$\frac{24a^{3}x^{2}}{16a^{2}b^{3}}$ 16a⁴b³=2ab²*8a³b

$\frac{x + y}{x - y} = \frac{x^{2}2xy + y^{2}}{x^{2} - y^{2}}$ x²+2xy+y²(x+y)²=(x+y)(x+y) (x-y)(x+y)=x²-y²

$\frac{2a - b}{a + b} = \frac{8a - 2b^{2}}{4a^{2} + 6ab + 2b^{2}}$ 8a²-2b²=(4a²-b²)=2(2a-b)(2a+b)

2(a+b)(2a+b)=4a²+6ab+2b²

$\frac{a^{2} + 3ab}{a^{2}b + 3ab}$=$\frac{a(a + 3b)}{a(ab + 3b} = \frac{a + 3b}{ab + 3b}$

$\frac{x^{2} - x - 6}{x^{2} + x - 2} = \frac{\left( x + 2 \right)(x - 3)}{\left( x + 2 \right)(x - 1)} = \frac{x - 3}{x - 1}\ $

$\frac{2x^{3} - 2y^{3}}{5x^{2} - 5y^{2}} = \frac{2\left( x - y \right)(x^{2} + xy + y^{2}}{5\left( x - y \right)(x + y)} = \frac{2(x^{2} + xy + y^{2}}{5(x + y)}$

$\frac{3x^{2}}{2ab^{2}}$=$\frac{24a^{3}x^{2}}{16a^{2}b^{3}}$ 16a⁴b³=2ab²*8a³b

$\frac{x + y}{x - y} = \frac{x^{2}2xy + y^{2}}{x^{2} - y^{2}}$ x²+2xy+y²(x+y)²=(x+y)(x+y) (x-y)(x+y)=x²-y²

$\frac{2a - b}{a + b} = \frac{8a - 2b^{2}}{4a^{2} + 6ab + 2b^{2}}$ 8a²-2b²=(4a²-b²)=2(2a-b)(2a+b)

2(a+b)(2a+b)=4a²+6ab+2b²

$\frac{a^{2} + 3ab}{a^{2}b + 3ab}$=$\frac{a(a + 3b)}{a(ab + 3b} = \frac{a + 3b}{ab + 3b}$

$\frac{x^{2} - x - 6}{x^{2} + x - 2} = \frac{\left( x + 2 \right)(x - 3)}{\left( x + 2 \right)(x - 1)} = \frac{x - 3}{x - 1}\ $

$\frac{2x^{3} - 2y^{3}}{5x^{2} - 5y^{2}} = \frac{2\left( x - y \right)(x^{2} + xy + y^{2}}{5\left( x - y \right)(x + y)} = \frac{2(x^{2} + xy + y^{2}}{5(x + y)}$

$\frac{3x^{2}}{2ab^{2}}$=$\frac{24a^{3}x^{2}}{16a^{2}b^{3}}$ 16a⁴b³=2ab²*8a³b

$\frac{x + y}{x - y} = \frac{x^{2}2xy + y^{2}}{x^{2} - y^{2}}$ x²+2xy+y²(x+y)²=(x+y)(x+y) (x-y)(x+y)=x²-y²

$\frac{2a - b}{a + b} = \frac{8a - 2b^{2}}{4a^{2} + 6ab + 2b^{2}}$ 8a²-2b²=(4a²-b²)=2(2a-b)(2a+b)

2(a+b)(2a+b)=4a²+6ab+2b²

$\frac{a^{2} + 3ab}{a^{2}b + 3ab}$=$\frac{a(a + 3b)}{a(ab + 3b} = \frac{a + 3b}{ab + 3b}$

$\frac{x^{2} - x - 6}{x^{2} + x - 2} = \frac{\left( x + 2 \right)(x - 3)}{\left( x + 2 \right)(x - 1)} = \frac{x - 3}{x - 1}\ $

$\frac{2x^{3} - 2y^{3}}{5x^{2} - 5y^{2}} = \frac{2\left( x - y \right)(x^{2} + xy + y^{2}}{5\left( x - y \right)(x + y)} = \frac{2(x^{2} + xy + y^{2}}{5(x + y)}$

$\frac{3x^{2}}{2ab^{2}}$=$\frac{24a^{3}x^{2}}{16a^{2}b^{3}}$ 16a⁴b³=2ab²*8a³b

$\frac{x + y}{x - y} = \frac{x^{2}2xy + y^{2}}{x^{2} - y^{2}}$ x²+2xy+y²(x+y)²=(x+y)(x+y) (x-y)(x+y)=x²-y²

$\frac{2a - b}{a + b} = \frac{8a - 2b^{2}}{4a^{2} + 6ab + 2b^{2}}$ 8a²-2b²=(4a²-b²)=2(2a-b)(2a+b)

2(a+b)(2a+b)=4a²+6ab+2b²