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Quadratic Equations

Find the prod...

Question

Find the product of the rational expressions $\frac{3 x^{2} + 8 x - 3}{2 x^{2} - x - 6}$ and $\frac{x^{2} - 4}{x + 3}$ .

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Solution

$\frac{3 x^{2} + 8 x - 3}{2 x^{2} - x - 6} \times \frac{x^{2} - 4}{x + 3}$

$= \frac{(x + 3) (3 x - 1)}{(2 x + 3) (x - 2)} \times \frac{(x - 2) (x + 2)}{(x + 3)}$

$= \frac{(3 x - 1) (x + 2)}{2 x + 3}$

$= \frac{3 x^{2} + 5 x - 2}{2 x + 3}$
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Q. Express the following rational expressions in its lowest term.

\frac{(x - 3) (x^{2} - 5 x + 4)}{(x - 4) (x^{2} - 2 x - 3)}

Q. Match the following.

	Column - I		Column - II
(P)	$(x^{2} + 5) (x^{3} + 3) + 5$	(1)	${- x}^{3} - 3 x^{2} + 3 x + 2$
(Q)	$(\frac{- 10}{3} x y^{3}) \times (\frac{6}{5} x^{3} y)$	(2)	$- x^{3} + x^{2} + 3 x - 6$
(R)	$(x^{3} - x^{2} - x - 2) - (2 x^{3} + 2 x^{2} - 4 x - 4)$	(3)	$x^{5} + 5 x^{3} + 3 x^{2} + 20$
(S)	$(x^{3} - x^{2} - x - 2) + (2 x^{2} - 2 x^{3} + 4 x - 4)$	(4)	$- 4 x^{4} y^{4}$

Q. Find the range of the rational expression

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: 2 x^{2} + 5 x - 1 + 8 x + x^{2} + 7 - 6 x + 3 - 3 x^{2}

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