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0
164
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Feb 10, 2019

#1
+57
+1

Multiply by the recriprocal of the algebraic expression you are trying to divide by.

Feb 10, 2019
#2
+4322
+1

1. I'll give a solution just for this one: Take the reciprocal like the user above had said.

1. $$\frac{2p}{4p^2-1}\times \frac{6p+3}{6p^3}$$

2. We realize that $$\frac{6p+3}{6p^3}=\frac{2p+1}{2p^3}.$$

3. We get: $$\frac{2p\left(2p+1\right)}{\left(4p^2-1\right)\times \:2p^3}$$.

4. And. $$\frac{p\left(2p+1\right)}{\left(4p^2-1\right)p^3}$$, so $$\frac{2p+1}{p^2\left(4p^2-1\right)}$$.

5. Factor: $$4p^2-1:\quad \left(2p+1\right)\left(2p-1\right)$$

6. Therefore, $$\frac{1}{p^2\left(2p-1\right)}$$ , consequently, $$p^2\left(2p-1\right):\quad 2p^3-p^2.$$

Thus, the final answer is $$\boxed{\frac{1}{2p^3-p^2}}.$$

.
Feb 10, 2019