Question

Simplify into factors (X/X+2)-(3/x-3)+(X+10/x²-4)​

Answer 1

$\huge\bf{{\color{black}{a}}{\color{maroon}{n}}{\red{s}}{\color{red}{w}}{\color{orange}{e}}{\color{gold}{r}}}$

$\tt (\frac{x}{x + 2}) - ( \frac{3}{x - 3} ) + ( \frac{x + 10}{ {x}^{2} - 4 } ) \\ \\ \tt = ( \frac{x(x - 3) - 3(x + 2)}{(x + 2)(x - 3)} ) + ( \frac{x + 10}{ {x}^{2} - 4 } ) \\ \\ \tt = ( \frac{ {x}^{2} - 3x -3x - 6 }{ {x}^{2} - 3x + 2x - 6 } ) + (\frac{x + 1 0 }{ {x}^{2} - 4 } ) \\ \\ \tt = ( \frac{ {x}^{2} - 9x - 6 }{ {x}^{2} - x - 6 } ) + ( \frac{x + 10}{ {x}^{2} - 4} ) \\ \\ \tt = ( \frac{9x}{x} ) + ( \frac{x + 10}{ {x}^{2} - 4 } ) \\ \\ \tt = ( \frac{9x( {x}^{2} - 4) + x(x + 10) }{x( {x}^{2} - 4)}) \\ \\ \tt = \frac{ {9 \cancel{x}}^{3} - \cancel{36}x^{9} + {x}^{2} + 10x }{ \cancel{x}^{3} - \cancel{4x}} \\ \\ \tt = 9 - 9 + {x}^{2} + 10x \\ \\ \tt = \underline{ \underline{{x}^{2} + 10x}}$

$\huge\bf{{\color{maroon}{Hope}}~{\color{red}{it}}~{\orange{helps..!!}}}$

Answer 2

Answer:

$\huge\bf{{\color{black}{a}}{\color{maroon}{n}}{\red{s}}{\color{red}{w}}{\color{orange}{e}}{\color{gold}{r}}}\\</p><p></p><p></p><p>\begin{gathered} \tt (\frac{x}{x + 2}) - ( \frac{3}{x - 3} ) + ( \frac{x + 10}{ {x}^{2} - 4 } ) \\ \\ \tt = ( \frac{x(x - 3) - 3(x + 2)}{(x + 2)(x - 3)} ) + ( \frac{x + 10}{ {x}^{2} - 4 } ) \\ \\ \tt = ( \frac{ {x}^{2} - 3x -3x - 6 }{ {x}^{2} - 3x + 2x - 6 } ) + (\frac{x + 1 0 }{ {x}^{2} - 4 } ) \\ \\ \tt = ( \frac{ {x}^{2} - 9x - 6 }{ {x}^{2} - x - 6 } ) + ( \frac{x + 10}{ {x}^{2} - 4} ) \\ \\ \tt = ( \frac{9x}{x} ) + ( \frac{x + 10}{ {x}^{2} - 4 } ) \\ \\ \tt = ( \frac{9x( {x}^{2} - 4) + x(x + 10) }{x( {x}^{2} - 4)}) \\ \\ \tt = \frac{ {9 \cancel{x}}^{3} - \cancel{36}x^{9} + {x}^{2} + 10x }{ \cancel{x}^{3} - \cancel{4x}} \\ \\ \tt = 9 - 9 + {x}^{2} + 10x \\ \\ \tt = \underline{ \underline{{x}^{2} + 10x}}\end{gathered}(x+2x)−(x−33)+(x2−4x+10)=((x+2)(x−3)x(x−3)−3(x+2))+(x2−4x+10)=(x2−3x+2x−6x2−3x−3x−6)+(x2−4x+10)=(x2−x−6x2−9x−6)+(x2−4x+10)=(x9x)+(x2−4x+10)=(x(x2−4)9x(x2−4)+x(x+10))=x3−4x9x3−36x9+x2+10x=9−9+x2+10x=x2+10x</p><p></p><p>\huge\bf{{\color{maroon}{Hope}}~{\color{red}{it}}~{\orange{helps..!!}}}Hope it helps..!!</p><p></p><p>$