Question 345404: Solve
3/x=8/x-1/11
Found 2 solutions by haileytucki, Fombitz:
Answer by haileytucki(390)   (Show Source):
You can put this solution on YOUR website! (3)/(x)=(8)/(x)-(1)/(11)
To add fractions, the denominators must be equal. The denominators can be made equal by finding the least common denominator (LCD). In this case, the LCD is 11x. Next, multiply each fraction by a factor of 1 that will create the LCD in each of the fractions.
(3)/(x)=(8)/(x)*(11)/(11)-(1)/(11)*(x)/(x)
Complete the multiplication to produce a denominator of 11x in each expression.
(3)/(x)=(88)/(11x)-(x)/(11x)
Combine the numerators of all expressions that have common denominators.
(3)/(x)=(88-x)/(11x)
Reorder the polynomial 88-x alphabetically from left to right, starting with the highest order term.
(3)/(x)=(-x+88)/(11x)
Since there is one rational expression on each side of the equation, this can be solved as a ratio. For example, (A)/(B)=(C)/(D) is equivalent to A*D=B*C.
3*11x=(-x+88)*x
Since x is on the right-hand side of the equation, switch the sides so it is on the left-hand side of the equation.
(-x+88)*x=3*11x
Multiply (-x+88) by x to get x(-x+88).
x(-x+88)=3*11x
Multiply 3 by 11x to get 33x.
x(-x+88)=33x
Multiply x by each term inside the parentheses.
-x^(2)+88x=33x
Since 33x contains the variable to solve for, move it to the left-hand side of the equation by subtracting 33x from both sides.
-x^(2)+88x-33x=0
Since 88x and -33x are like terms, add -33x to 88x to get 55x.
-x^(2)+55x=0
Multiply each term in the equation by -1.
x^(2)-55x=0
Factor out the GCF of x from each term in the polynomial.
x(x)+x(-55)=0
Factor out the GCF of x from x^(2)-55x.
x(x-55)=0
Set the single term factor on the left-hand side of the equation equal to 0.
x=0
Set each of the factors of the left-hand side of the equation equal to 0.
x-55=0
Since -55 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 55 to both sides.
x=55
The complete solution is the set of the individual solutions.
x=0,55
Check that all solutions found are valid and are part of the domain by substituting them into the original equation.
x=55
Answer by Fombitz(32388)  (Show Source):
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