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(2ax^(2)+ax)/(a^(2)x^(3)-x)*(ax+1)/(2x+1)= ?

$37$ . $\frac{2 a x^{2}+a x}{a^{2} x^{3}-x} \cdot \frac{a x+1}{2 x+1}=$ ?

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Evaluate integers raised to rational exponents

Full solution

Q.

37

.

\frac{2 a x^{2}+a x}{a^{2} x^{3}-x} \cdot \frac{a x+1}{2 x+1}=

?

Factor out $ax$ : Factor out $ax$ from the numerator of the first fraction and $x$ from the denominator. $\frac{ax(2x+1)}{x(a^2x^2-1)}\cdot\frac{ax+1}{2x+1}$
Factor difference of squares: Notice that $a^2x^2-1$ is a difference of squares and can be factored as $ax+1$ $ax-1$ . rac{ax(2x+1)}{x(ax+1)(ax-1)}rac{ax+1}{2x+1}
Cancel out terms: Cancel out the $(2x+1)$ terms in the numerator of the first fraction and the denominator of the second fraction. $\frac{ax}{x(ax+1)(ax-1)}\times(ax+1)$
Cancel out terms: Cancel out the $(ax+1)$ terms in the denominator of the first fraction and the numerator of the second fraction. $\frac{ax}{x(ax-1)}$
Cancel out terms: Cancel out the $x$ terms in the numerator and the denominator. $\frac{a}{ax-1}$
Final simplification: Realize that we can't simplify further since there's no common factor left.

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