Question

x²-3x/x²+3x-10 x x²-4/x²-x-6 rational algebraic expression. with a concrete solutions​

Answer 1

SOLUTION

TO SIMPLIFY

$\displaystyle \sf{ \frac{ {x}^{2} - 3x }{ {x}^{2} + 3x - 10 } \: \times \: \frac{ {x}^{2} - 4}{ {x}^{2} - x - 6} }$

EVALUATION

Here the given expression is

$\displaystyle \sf{ \frac{ {x}^{2} - 3x }{ {x}^{2} + 3x - 10 } \: \times \: \frac{ {x}^{2} - 4}{ {x}^{2} - x - 6} }$

We simplify it as below

$\displaystyle \sf{ \frac{ {x}^{2} - 3x }{ {x}^{2} + 3x - 10 } \: \times \: \frac{ {x}^{2} - 4}{ {x}^{2} - x - 6} }$

$\displaystyle \sf{ = \frac{ x(x - 3) }{ {x}^{2} + (5 - 2)x - 10 } \: \times \: \frac{ {x}^{2} - {2}^{2} }{ {x}^{2} - (3 - 2)x - 6} }$

$\displaystyle \sf{ = \frac{ x(x - 3) }{ {x}^{2} + 5x - 2x - 10 } \: \times \: \frac{ {x}^{2} - {2}^{2} }{ {x}^{2} - 3x + 2x - 6} }$

$\displaystyle \sf{ = \frac{ x(x - 3) }{ x(x + 5) - 2(x + 5) } \: \times \: \frac{(x + 2)(x - 2) }{ x(x - 3) + 2(x - 3)} }$

$\displaystyle \sf{ = \frac{ x(x - 3) }{ (x + 5) (x - 2) } \: \times \: \frac{(x + 2)(x - 2) }{ (x - 3) (x + 2)} }$

$\displaystyle \sf{ = \frac{ x }{ (x + 5) } }$

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