Solve: x/(x−3)=2x/(x−3)−5/3

Question

Accepted Answer

Welcome back. I am so glad you're here. We are Given the equation A divided by a minus eight equals three. A divided by a minus eight minus 14 divided by three. And we're asked to solve for a well the first thing I would like to do is get rid of all these fractions. So we're going to do that by multiplying everything by the common denominator. What would the common denominator be? It will be an a -8 times three. And now we can rewrite this. So distributing that a minus eight times three. So we've got a times a minus eight times three and it's good to keep everything in factors for a while here, that's divided by a minus eight equals three A times a minus eight times three. All over still a minus eight minus 14 times a minus eight times three. All over three. And now the absolute most glorious part of all math is canceling out factors that occur in both the numerator and the denominator. So on the left hand side of the equal sign, the a minus eight cancel out for that fraction. The first fraction on the right hand side of the equal sign a minus eight's cancel out. And the second fraction over there, the three's cancel out. So now this reads three times A. On the left. Well that's three A equals 38 times three. Well that's nine a minus 14 times that a minus eight. Now we can distribute that 14 times a minus eight will bring down three A equals nine a -14 times eight is 14 a and negative. 14 times negative eight equals positive 112. Now we want to combine like terms, so we've got this nine A minus 14 A. Which will be a negative five A Plus 112. Bring that down and bring down the three a. Now we can add 58 both sides to get the A's together And we've got eight a. equals 112. And now dividing both sides by eight and we get A equals 14. We look at our answer choices and this matches with answer choice C. Well done, we'll catch you on the next one.

Solve: x/(x−3)=2x/(x−3)−5/3

Key Concepts

Rational Expressions

Cross Multiplication

Solving Linear Equations

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