Question

निम्नलिखित परिमेय व्यंजक का गुणनफल ज्ञात कीजिए तथा उनके निम्नतम रूप में व्यक्त कीजिए

$\frac{ax - {x}^{2} }{a {}^{2} + 2ax + {x}^{2} } \: \frac{ {a}^{2} + ax }{ {a}^{2} - 2ax + {x}^{2} }$

Answer 1

हल-

युग्मो का गुणनफल = $\frac{ax - {x}^{2} }{a {}^{2} + 2ax + {x}^{2} } \: \frac{ {a}^{2} + ax }{ {a}^{2} - 2ax + {x}^{2} }$


$\frac{x(a - x)}{( {a + x)}^{2} } \times \frac{a(a + x)}{(a - x) {}^{2} } \\ \\ = \frac{a x}{(a + x)(a - x)} \\ \\ = \frac{ax}{ {a}^{2} - {x}^{2} }$

अतः अभीष्ट गुणनफल का निम्नतम रूप

$= \frac{ax}{ {a}^{2} - {x}^{2} }$

Answer 2

$\huge\boxed{\texttt{\fcolorbox{Red}{aqua}{Hey Mate!!!!}}}$

$<b>$
Here is your answer.
$\frac{ax - x {}^{2} }{a {}^{2} + 2ax + x {}^{2} } \times \frac{a {}^{2} + ax }{a {}^{2} - 2ax + x {}^{2} } \\ = \frac{x(a - x)}{(a + x) {}^{2} } \times \frac{a(a + x)}{(a - x) {}^{2} } \\ = \frac{ax}{(a + x)(a - x)} \\ = \frac{ax}{a {}^{2} - x {}^{2} }$
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