Using rational functions solve
7+ (1)/x = 1/(x-2)
thank you
To solve the given rational equation, follow these steps:
Step 1: Identify the denominators and find the least common denominator (LCD).
In this case, the denominators are 'x' and 'x - 2'. The LCD is the product of the two denominators, which is 'x(x - 2)'.
Step 2: Multiply both sides of the equation by the LCD to clear the fractions.
Multiplying each term by 'x(x - 2)', we get:
7x(x - 2) + (x)(x - 2) = (x)(x - 2)
Step 3: Simplify the equation by expanding and combining like terms.
Expanding the equation, we have:
7x^2 - 14x + x^2 - 2x = x^2 - 2x
Combining like terms, we get:
8x^2 - 16x = x^2 - 2x
Step 4: Move all terms to one side of the equation to get a quadratic equation in standard form.
By subtracting 'x^2' and adding '2x' from both sides, we get:
8x^2 - x^2 - 16x + 2x = 0
Simplifying further, we have:
7x^2 - 14x = 0
Step 5: Factor out common terms, if possible.
Factoring out '7x' from both terms, we get:
7x(x - 2) = 0
Step 6: Apply the zero-product property by setting each factor equal to zero.
Setting 7x = 0, we find:
x = 0
Setting (x - 2) = 0, we find:
x - 2 = 0
x = 2
Therefore, the solutions to the given equation are x = 0 and x = 2.