How do you solve #1 + (2+xy)/(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+xy)/(x+y) = 2/y, we can follow these steps:

Multiply both sides of the equation by y(x+y) to eliminate the denominators. This gives us: y(x+y) + (2+xy) = 2(x+y)

Expand the equation by distributing the terms: yx + y^2 + 2 + x  y = 2x + 2y

Rearrange the equation by grouping like terms: yx + x  2x + y^2  y  2y = 2

Combine like terms: (yx  x  2x) + (y^2  y  2y) = 2

Simplify further: (yx  3x) + (y^2  3y) = 2

Rearrange the equation to bring all terms to one side: yx  3x + y^2  3y + 2 = 0

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 onesided 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 onesided 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 onesided 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 onesided 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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