how do you solve 3/x+x/10=11/2x

Question

it is not addition but multiplyign a common factor from the numerator. the answer is 10x

Answer 1

Hi Alexis,

 

A common method for solving equations involving fractions is to "get rid of the fractions". That can be done by multiplying both sides of the equation by the LCD of all the denominators that appear in the fraction.

 

In this case the denominators are : x, 10, and 2x. The LCD is indeed 10x because all three denominators divide evenly into that expression.

 

To understand why we pick 10x as the multiplier look what happens:

 

10x times 3/x become 30, because the denominator x divides into the multiplier leaving a factor of 10, and 10 times 3 = 30.

 

Similarly 10x time x/10 results in x². 

 

Finally 10x times 11/2x results in 55.

 

What we are doing is this:

 

10x (3/x + x/10) = 10x (11/2x).

 

30 + x² = 55

 

x² = 25

 

Therefore x = +5 or -5. Two answers for x. Try substituting each into the original equation to confirm both work.

Answer 2

(3/x)+(x/10)=(11/2x)

multiply both sides by 10x, the LCD

10x(3/x)+10x(x/10)=10x(11/2x)

30+x^2=55

x^2=55-30

x^2=25

take the square root of both sides

±x=5

x=+5 and

x=-5