Solve for X: x-1 x+3 5 ---- + ----= - 2x 4x 8

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Solve for X: x-1 x+3 5 ---- + ----= - 2x 4x 8

Mathematics
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is the last thing a negative or positive fraction?
positive fraction
Multiply each term by a factor of 1 that will equate all the denominators. In this case, all terms need a denominator of 4x. The expression needs to be multiplied by to make the denominator 4x. Multiply the expression by a factor of 1 to create the least common denominator (LCD) of 4x. Multiply 2 by each term in x-1 to get 2x-2. The numerators of expressions that have equal denominators can be combined. In this case, and have the same denominator of 4x, so the numerators can be combined. Simplify the numerator of the expression. Combine all similar terms in the polynomial 2x-2+x+3. Find the LCD (least common denominator) of Least common denominator: 8x Multiply each term in the equation by 8x in order to remove all the denominators from the equation. Simplify the left-hand side of the equation by canceling the common factors. Simplify the equation. 6x+2=5x Since 5x contains the variable to solve for, move it to the left-hand side of the equation by subtracting 5x from both sides. 6x+2-5x=0 Since 6x and -5x are like terms, add -5x to 6x to get x. x+2=0 Since 2 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 2 from both sides. x=-2

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\[\frac{ x -1 }{ 2x }+\frac{ x +3 }{ 4x }=\frac{ 5 }{ 8 }\] Multiply both sides of the equation by 8x (the least common multiple of the denominators). \[4(x -1)+2(x +3)=5x\] \[4x -4+2x +6=5x\] \[4x +2x -5x =4-6\] \[x =-2\]
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