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Equivalent Fractions with Expressions

Say I wanted to write 3 divided by 4x as an equivalent fraction with a denominator of 8 times x squared times x plus 2. What I must first do is ask myself, "What do I need to multiply 4x by to get 8x squared times x plus 2?" Well, I know that 4 times 2 equals 8. I also know that x times x equals x squared. It looks like we are missing an x plus 2, so we have to place the x plus 2 in the denominator as well. So, what I multiply the denominator by, I also what I multiply the numerator by to maintain equivalency. So, I am going to simply rewrite that at the top. Now all I have to do is just multiply straight across the numerator. So, 3 times 2 equals 6, and simply write down the x times x plus 2.

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