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

Suzhoumeite

2 min read

·

Jun 07, 2024

23

Share

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

The given equation is a rational expression, and we need to find the values of x that satisfy the equation. Let's start by simplifying the equation.

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

To simplify the equation, we can start by multiplying the numerators and denominators separately.

(2x - 14 + x^2 - 7x)/(x^2 - x - 20) = 1

Now, we can cross-multiply to eliminate the fractions.

x^2 - 7x - 14 = x^2 - x - 20

Let's simplify the equation further by combining like terms.

-7x - 14 = -x - 20

-6x = -6

x = 1

Therefore, the value of x that satisfies the equation is x = 1.

Checking the Solution

Let's plug in x = 1 back into the original equation to verify our solution.

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

(3)(-6)/(-4)(5) = ?

18/20 = 9/10 = 1

The solution checks out, and we have confirmed that the value of x that satisfies the equation is indeed x = 1.