Video: Adding Algebraic Fractions with 𝑥 in the Numenrator

Simplify 2𝑥/5 + 3𝑥/4.

01:07

Video Transcript

Simplify two 𝑥 over five plus three 𝑥 over four. So again those denominators don’t have any common factors other than one, so I’m gonna have to multiply both of the fractions by some version of one in order to get equivalent fractions. And I’m gonna multiply the second fraction by five over five, and I’m gonna multiply the first fraction by four over four. And now I’ve got common denominators of four over four times five in each case. And because I’ve got those common denominators, I can merge those two fractions into one. So I’ve got four lots of two 𝑥 plus five lots of three 𝑥 all over four times five, so let’s evaluate some of those. Well four times two 𝑥 is eight 𝑥, five times three 𝑥 is fifteen 𝑥, so we’re adding fifteen 𝑥, and four times five on the bottom is twenty. And eight 𝑥 plus fifteen 𝑥 is twenty-three 𝑥. Nothing cancels down, so that’s our answer.

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