# Video: US-SAT03S4-Q06-378185749452

Which of the following is equivalent to π₯β»Β² ((π₯ + π₯)/(π₯ + π₯ + π₯))? [A] 2/3π₯ [B] 1/π₯ [C] 3/2π₯ [D] 2/3π₯Β²

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### Video Transcript

Which of the following is equivalent to π₯ to the negative two power times π₯ plus π₯ over π₯ plus π₯ plus π₯? A) Two over three π₯, B) one over π₯, C) three over two π₯, or D) two over three π₯ squared.

At this point, we have to remember what we do when weβre adding variables together. π₯ plus π₯ equals two π₯. Its exponent, its power, doesnβt change. If you canβt remember what to do here, try substituting numbers. If you had three plus three, that would equal two times three. It wouldnβt equal three squared. Once that squared away, we know that, in the denominator, π₯ plus π₯ plus π₯ equals three π₯. Bring down our π₯ to the negative two power. At this point, in our fraction, we have an π₯ over π₯. And those values cancel out, because π₯ over π₯ just equals one. So we have two-thirds times π₯ to the negative two power. π₯ to the negative two power can be written as one over π₯ squared. Multiply that by two-thirds. When weβre multiplying fractions, we multiply their numerators. One times two is two. And π₯ squared times three is three π₯ squared.

Two over three π₯ squared is equivalent to the expression we started with. And thatβs option D.