How do you solve #1 + (2+x-y)/(x+y) = 2/y#?
To combine the fractions, first rearrange the equation as follows:
Multiply the denominators by 2. You can do this in one step, but I've done it in two to illustrate the exact process:
Simplify:
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To solve the equation 1 + (2+x-y)/(x+y) = 2/y, we can follow these steps:
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Multiply both sides of the equation by y(x+y) to eliminate the denominators. This gives us: y(x+y) + (2+x-y) = 2(x+y)
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Expand the equation by distributing the terms: yx + y^2 + 2 + x - y = 2x + 2y
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Rearrange the equation by grouping like terms: yx + x - 2x + y^2 - y - 2y = -2
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Combine like terms: (yx - x - 2x) + (y^2 - y - 2y) = -2
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Simplify further: (yx - 3x) + (y^2 - 3y) = -2
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Rearrange the equation to bring all terms to one side: yx - 3x + y^2 - 3y + 2 = 0
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This quadratic equation can be solved by factoring, completing the square, or using the quadratic formula.
Note: The specific values of x and y that satisfy the equation will depend on the solutions obtained from the quadratic equation.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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