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How to solve and respond.

How to solve and respond.-example-1
User Insomiac
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1 Answer

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18 votes

Explanation:

the error:

it is stated that


(5x)/(x+7) +(7)/(x) = (5x)/(x+7) +(7(7))/(x+7)

subtract (5x)/(x+7) from both sides


(7)/(x) = (7(7))/(x+7)

multiply both sides by x + 7

7(x+7) = 49x

7x + 49 = 49x

subtract 7x from both sides to isolate x and its coefficient

49 = 42x

thus, this is only true when 49 = 42x. in order for these two equations to be equal, they must always be true, so this is wrong

the solution:

we want to express 7/x as (something) / (x+7). to do this, we can multiply 7/x by 1.

anything divided by itself = 1. thus, if we multiply both the numerator and the denominator by something that turns x into (x+7), we can do what we want to do.

(x+7)/x * x turns x into (x+7), so we multiply both the numerator and denominator by (x+7)/x to get


(7)/(x) = (7(x+7)/x)/(x+7)

substitute this for 7/x in our original problem


(5x)/(x+7) +(7(x+7)/x)/(x+7) = (5x)/(x+7) +((7x+49)/x)/(x+7) = (5x)/(x+7) +(7+49/x)/(x+7) = (5x+7+49/x)/(x+7)

User BlackMagic
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