Asap Po Plzzzzzzz With Solution Din Po Sana Thank You (1)

Asap po plzzzzzzz with solution din po sana thank you (1)

 

(63)

\dfrac{1}{x^2-4}\div\dfrac{x^2+6x+9}{x^2+x-6}\\\\\\=\dfrac{1}{x^2-4}\times\dfrac{x^2+x-6}{x^2+6x+9}\\\\\\=\dfrac{1}{x^2-2^2}\times\dfrac{x^2+3x-2x-6}{x^2+(2\times3x)+3^2}\\\\\\=\dfrac{1}{(x+2)(x-2)}\times\dfrac{x(x+3)-2(x+3)}{(x+3)^2}\\\\\\=\dfrac{1}{(x+2)(x-2)}\times\dfrac{(x+3)(x-2)}{(x+3)(x+3)}\\\\\\=\dfrac{1}{(x+2)(x+3)}

(64)

\dfrac{5x+5y}{x^2-9y^2}\div\dfrac{10x+10y}{x-3y}\\\\\\=\dfrac{5(x+y)}{x^2-(3y)^2}\div\dfrac{10(x+y)}{x-3y}\\\\\\=\dfrac{5(x+y)}{x^2-(3y)^2}\times\dfrac{x-3y}{ 10(x+y)}\\\\\\=\dfrac{1}{(x+3y)(x-3y)}\times\dfrac{(x-3y)}{2}\\\\\\=\dfrac{1}{2(x+3y)}

(65)

\dfrac{x}{x^2+2x-x-2}-\dfrac{1}{x+2}\\\\\\=\dfrac{x}{x(x+2)-2(x+2)}-\dfrac{1}{x+2}\\\\\\=\dfrac{x}{(x+2)(x-2)}-\dfrac{(x-2)}{(x+2)(x-2)}\\\\\\=\dfrac{x-(x-2)}{(x+2)(x-2)}\\\\\\=\dfrac{x-x+2}{(x+2)(x-2)}\\\\\\=\dfrac{2}{(x+2)(x-2)}

(66)

\dfrac{10}{x^2-x}-\dfrac{3}{x^2-1^2}\\\\\\=\dfrac{10}{x(x-1)}-\dfrac{3}{(x+1)(x-1)}\\\\\\=\dfrac{10(x+1)}{x(x+1)(x-1)}-\dfrac{3x}{x(x+1)(x-1)}\\\\\\=\dfrac{10x+10-3x}{x(x+1)(x-1)}\\\\\\=\dfrac{7x+10}{x(x+1)(x-1)}

(67)

\dfrac{4x}{x^2-4}+\dfrac{2x}{x+2}\\\\\\=\dfrac{4x}{x^2-2^2}+\dfrac{2x}{x+2}\\\\\\=\dfrac{4x}{(x+2)(x-2)}+\dfrac{2x(x-2)}{(x+2)(x-2)}\\\\\\=\dfrac{4x+2x(x-2)}{(x+2)(x-2)}\\\\\\=\dfrac{4x+2x^2-4x}{(x+2)(x-2)}\\\\\\=\dfrac{2x^2}{(x+2)(x-2)}

(68)

\dfrac{3}{2x}+\dfrac{9}{5x}\\\\\\=\dfrac{3\times5}{2x\times5}+\dfrac{9\times2}{5x\times2}\\\\\\=\dfrac{15}{10x}+\dfrac{18}{10x}\\\\\\=\dfrac{(15+18)}{10x}=\dfrac{33}{10x}

(69)

\dfrac{\dfrac{1}{a}-\dfrac{1}{b}}{\dfrac{3}{ab}}\\\\\\=\dfrac{\Big(\dfrac{b-a}{\diagup\!\!\!\!\!{ab}}\Big)}{\Big(\dfrac{3}{\diagup\!\!\!\!\!{ab}}\Big)}\\\\\\=\dfrac{b-a}{3}

(70)

\dfrac{\dfrac{5}{a}-\dfrac{2}{b}}{\dfrac{3}{a^2}-\dfrac{2}{b^2}}\\\\\\=\dfrac{\Big(\dfrac{5b-2a}{ab}\Big)}{\Big(\dfrac{3b^2-2b^2}{a^2b^2}\Big)}\\\\\\=\dfrac{5b-2a}{ab}\times\dfrac{(ab)^2}{3b^2-2a^2}\\\\\\=\dfrac{ab(5b-2a)}{3b^2-2b^2}


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