Final answer:
To solve the rational equations: a) (x + 2)/(x - 1) = 0, we set the numerator x + 2 equal to zero and solve for x to get x = -2. For b) 1/x + 1/y = 0, we find a common denominator xy and solve for y to get y = -x. For c) x/y = y/x, this equation is always true for any values of x and y. For d) 2x/(x + 1) = 1, we cross-multiply and solve for x to get x = -1.
Step-by-step explanation:
To solve the given rational equations:
a) (x + 2)/(x - 1) = 0
To solve this equation, we set the numerator equal to zero, since a fraction is only equal to zero when the numerator is zero. So, (x + 2) = 0. Solving for x, we get x = -2.
b) 1/x + 1/y = 0
To solve this equation, we need to find a common denominator for the fractions. Remember that the LCD (Least Common Denominator) is the product of the denominators. So, the common denominator is xy. Multiplying both sides of the equation by xy, we get y + x = 0. Rearranging the equation, we have y = -x.
c) x/y = y/x
To solve this equation, we cross-multiply, which means we multiply x by y and y by x. So, xy = yx. Since multiplication is commutative, this equation is always satisfied. Therefore, for any value of x and y, this equation is true.
d) 2x/(x + 1) = 1
To solve this equation, we cross-multiply, which means we multiply 2x by 1 and (x + 1) by 1. So, 2x = x + 1. Solving for x, we subtract x from both sides and subtract 1 from both sides to get x = -1.