solve the equation 3/ (x+1) - 1/x =1/2
multiply each term by 2x(x+1)
6x - 2(x+1) = x(x+1)
6x - 2x - 2 = x^2 + x
x^2 +3x + 2 = 0
(x-1)(x-3) = 0
x = 1 or x = 3
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18) In October, a hardware store purchased snow shovels for $8 each. The original markup was 50% based on the selling price. In December, the store had a sale and marked down the shovels by 20%. By January 1, the sale was over and the shovels were marked up 15%. In March, the store held a clearance sale of all winter tools by having a final markdown of 60%. What was the final selling price of the shovels? (Round to the nearest cent.)
To solve the equation (3 / (x + 1)) - (1 / x) = 1/2 for x, we will follow these steps:
Step 1: Clear the fractions by finding a common denominator.
Multiply the entire equation by 2x(x + 1) to eliminate the fractions:
2x(x + 1) * (3 / (x + 1)) - 2x(x + 1) * (1 / x) = 2x(x + 1) * (1/2)
Simplifying:
6x - 2(x + 1) = x(x + 1)
Step 2: Simplify and rearrange the equation.
Distribute 2 into (x + 1):
6x - 2x - 2 = x^2 + x
Combine like terms:
4x - 2 = x^2 + x
Rearrange the equation:
x^2 + x - 4x + 2 = 0
Combine like terms:
x^2 - 3x + 2 = 0
Step 3: Factor or use the quadratic formula to solve for x.
This equation can be factored as follows:
(x - 1)(x - 2) = 0
Setting each factor equal to zero:
x - 1 = 0 -> x = 1
x - 2 = 0 -> x = 2
So the equation has two solutions: x = 1 and x = 2.