Question 346976
x=(4+y)/(3-y)
First, we can solve for Y

Since y is on the right-hand side of the equation, switch the sides so it is on the left-hand side of the equation.
(4+y)/(3-y)=x

Since the variable is in the denominator on the left-hand side of the equation, this can be solved as a ratio.  For example, (A)/(B)=C is equivalent to (A)/(C)=B.
(y+4)/(x)=(-y+3)

Remove the parentheses around the expression -y+3.
(y+4)/(x)=-y+3

Find the LCD (least common denominator) of ((y+4))/(x)-y+3.
Least common denominator: x

Multiply each term in the equation by x in order to remove all the denominators from the equation.
(y+4)/(x)*x=-y*x+3*x

Simplify the left-hand side of the equation by canceling the common factors.
y+4=-y*x+3*x

Simplify the right-hand side of the equation by multiplying out all the terms.
y+4=-xy+3x

Since -xy contains the variable to solve for, move it to the left-hand side of the equation by adding xy to both sides.
y+4+xy=3x

Move all terms not containing y to the right-hand side of the equation.
xy+y+4=3x

Factor out the GCF of y from each term in the polynomial.
y(x)+y(1)=3x-4

Factor out the GCF of y from xy+y.
y(x+1)=3x-4

Divide each term in the equation by (x+1).
(y(x+1))/(x+1)=(3x)/(x+1)-(4)/(x+1)

Simplify the left-hand side of the equation by canceling the common factors.
y=(3x)/(x+1)-(4)/(x+1)

Simplify the right-hand side of the equation by simplifying each term.
y=(3x-4)/(x+1)



To solve for x
x=(4+y)/(3-y)

Reorder the polynomial 3-y alphabetically from left to right, starting with the highest order term.
x=(y+4)/(-y+3)


Now,
 to find the x an y intercepts, you can :

x=(4+y)/(3-y)

To find the x-intercept, substitute in 0 for y and solve for x.
x=(4+(0))/(3-(0))

Remove the parentheses around the expression 0.
x=(4+0)/(3-(0))

Add 0 to 4 to get 4.
x=(4)/(3-(0))

Multiply -1 by the 0 inside the parentheses.
x=(4)/(3+0)

Add 0 to 3 to get 3.
x=(4)/(3)

To find the y-intercept, substitute in 0 for x and solve for y.
(0)=(4+y)/(3-y)

Since y is on the right-hand side of the equation, switch the sides so it is on the left-hand side of the equation.
(4+y)/(3-y)=(0)

Remove the parentheses around the expression 0.
(y+4)/(-y+3)=0

Find the LCD (least common denominator) of ((y+4))/((-y+3))+0.
Least common denominator: (-y+3)

Multiply each term in the equation by (-y+3) in order to remove all the denominators from the equation.
(y+4)/(-y+3)*(-y+3)=0*(-y+3)

Simplify the left-hand side of the equation by canceling the common factors.
y+4=0*(-y+3)

Simplify the right-hand side of the equation by multiplying out all the terms.
y+4=0

Since 4 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 4 from both sides.
y=-4

These are the x and y intercepts of the equation x=((4+y))/((3-y)).
x=(4)/(3), y=-4

Hope this helps;-)
Jen