Using rational functions solve
7+ 1(numerator) x (denominator) = 1 (numerator) x-2(demominator)
To solve the given rational function equation, let's follow these steps:
Step 1: Start by multiplying both sides of the equation by the common denominator to get rid of the fractions. In this case, the common denominator is (denominator) on both sides.
7 + 1(numerator) x (denominator) = 1 (numerator) x -2(denominator)
Multiply both sides by (denominator):
(denominator) * (7 + 1(numerator) x (denominator)) = (denominator) * (1 (numerator) x -2(denominator))
Step 2: Distribute the denominator on both sides:
(7 x (denominator)) + (1(numerator) x (denominator)^2) = (1 (numerator) x -2(denominator) x (denominator))
(7(denominator)) + (1(numerator) x (denominator)^2) = (-2(denominator) x (denominator))
Step 3: Simplify the equation by combining like terms:
7(denominator) + (denominator^2)(numerator) = (-2(denominator^2))
Step 4: Rearrange the equation to make it equal to zero:
(denominator^2)(numerator) + (7(denominator) + 2(denominator^2)) = 0
Now the equation is in standard quadratic form ax^2 + bx + c = 0, where a = (numerator), b = 7(denominator), and c = 2(denominator^2)
Step 5: Solve the equation. You can use the quadratic formula to find the solutions. The quadratic formula is given as:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = (numerator), b = 7(denominator), and c = 2(denominator^2)
Plug in these values into the quadratic formula, and you'll get the solutions for x.