(2+x)(x-7)/(x-5)(x+4)=1

2 min read Jun 16, 2024

Solving the Equation: (2+x)(x-7)/(x-5)(x+4) = 1

This equation presents a rational equation with variables in both the numerator and denominator. Let's solve it step-by-step:

1. Eliminate the Fractions

To get rid of the fractions, we can multiply both sides of the equation by the denominator of the left side:

(2+x)(x-7) = (x-5)(x+4)

2. Expand and Simplify

Expand both sides of the equation:

2x - 14 + x² - 7x = x² - x - 20

Simplify by combining like terms:

-5x - 14 = -x - 20

3. Isolate the Variable

Move all the x terms to one side and the constant terms to the other:

-5x + x = -20 + 14

-4x = -6

4. Solve for x

Divide both sides by -4:

x = -6 / -4

x = 3/2

Conclusion

Therefore, the solution to the equation (2+x)(x-7)/(x-5)(x+4) = 1 is x = 3/2.

Important Note: It's crucial to check the solution by plugging it back into the original equation. In this case, we need to make sure that the denominator doesn't become zero when x = 3/2. Since it doesn't, our solution is valid.