How do you solve #1 + (2+x-y)/(x+y) = 2/y#?

Answer 1

#x=0# or #y=1#

To combine the fractions, first rearrange the equation as follows:

#1=2/y-(2+x-y)/(x+y)#

Multiply the denominators by 2. You can do this in one step, but I've done it in two to illustrate the exact process:

Multiply out #x+y#:
#1(x+y)=(2(x+y))/y-(2+x-y)#
Multiply out the #y#:
#1(x+y)y=2(x+y)-y(2+x-y)#

Simplify:

#xy+y^2=2x+2y-2y-xy+y^2#
#xy+xy+cancel(y^2)=2x+cancel(2y)-cancel(2y)+cancel(y^2)#
#2xy=2x#
#2xy-2x=0#
#2x(y-1)=0#
and dividing by #2# we get #x(y-1)=0#
as product of #x# and #(y-1)# is #0#. we have
#x=0# or #y=1#
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Answer 2

To solve the equation 1 + (2+x-y)/(x+y) = 2/y, we can follow these steps:

  1. 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)

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

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

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

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

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

  7. 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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Answer from HIX Tutor

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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