a) [tex]\cfrac{22p^4q^2}{99p^5q} = \cfrac{22q}{99p};[/tex]b) [tex]\cfrac{7a}{a^2+5a} = \cfrac{7a}{a(a+5)} = \cfrac{7}{a+5};[/tex]c) [tex]\cfrac{x^2-y^2}{4x+4y} = \cfrac{(x+y)(x-y)}{4(x+y)} = \cfrac{x-y}{4}.[/tex]
a) [tex]\cfrac{y-20}{4y}+\cfrac{5y-2}{y^2} = \cfrac{y(y-20)}{4y} + \cfrac{5y(y-2)}{y^2} = \cfrac{(y-20) + 5(y-2)}{4y} = \cfrac{6y-30}{4y} = \cfrac{3}{2};[/tex]b) [tex]\cfrac{1}{5c-d}-\cfrac{1}{5c+d} = \cfrac{1(5c+d) - 1(5c-d)}{(5c-d)(5c+d)} = \cfrac{5c+d - (5c-d)}{25c^2 - d^2} = \cfrac{2d}{25c^2 - d^2};[/tex]c) [tex]\cfrac{7}{a+5}-\cfrac{7a-3}{a^2+5a} = \cfrac{7(a^2+5a) - (7a-3)(a+5)}{(a+5)(a^2+5a)} = \cfrac{7a^2 + 35a - 7a^2 - 35a + 3}{a^2+5a} = \cfrac{3}{a^2+5a} = \cfrac{3}{a(a+5)}.[/tex]
a) [tex]\cfrac{22p^4q^2}{99p^5q} = \cfrac{22q}{99p};[/tex]
b) [tex]\cfrac{7a}{a^2+5a} = \cfrac{7a}{a(a+5)} = \cfrac{7}{a+5};[/tex]
c) [tex]\cfrac{x^2-y^2}{4x+4y} = \cfrac{(x+y)(x-y)}{4(x+y)} = \cfrac{x-y}{4}.[/tex]
a) [tex]\cfrac{y-20}{4y}+\cfrac{5y-2}{y^2} = \cfrac{y(y-20)}{4y} + \cfrac{5y(y-2)}{y^2} = \cfrac{(y-20) + 5(y-2)}{4y} = \cfrac{6y-30}{4y} = \cfrac{3}{2};[/tex]
b) [tex]\cfrac{1}{5c-d}-\cfrac{1}{5c+d} = \cfrac{1(5c+d) - 1(5c-d)}{(5c-d)(5c+d)} = \cfrac{5c+d - (5c-d)}{25c^2 - d^2} = \cfrac{2d}{25c^2 - d^2};[/tex]
c) [tex]\cfrac{7}{a+5}-\cfrac{7a-3}{a^2+5a} = \cfrac{7(a^2+5a) - (7a-3)(a+5)}{(a+5)(a^2+5a)} = \cfrac{7a^2 + 35a - 7a^2 - 35a + 3}{a^2+5a} = \cfrac{3}{a^2+5a} = \cfrac{3}{a(a+5)}.[/tex]