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

2 min read Jun 07, 2024

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

In this article, we will verify the equation:

$\frac{(2+x)(x-7)}{(x-5)(x+4)}=1$

To verify this equation, we will start by simplifying the left-hand side of the equation.

Let's start by multiplying the numerators and denominators separately:

$\frac{(2+x)(x-7)}{(x-5)(x+4)}=\frac{2x-x^2+14+7x-49}{x^2-5x-20}$

Now, let's simplify the numerator and denominator separately:

Numerator:

$2x-x^2+14+7x-49=-x^2+9x-35$

Denominator:

$x^2-5x-20$

So, the equation becomes:

$\frac{-x^2+9x-35}{x^2-5x-20}=1$

Now, let's verify if the equation is true. We can do this by cross-multiplying:

$-(x^2-9x+35)=x^2-5x-20$

Expanding and simplifying, we get:

$-x^2+9x-35=x^2-5x-20$

Rearranging the equation, we get:

$2x^2-14x+15=0$

Factoring the quadratic equation, we get:

$(x-3)(2x-5)=0$

This gives us two possible values for x:

$x=3\quad\text{or}\quad x=\frac{5}{2}$

We have successfully verified the equation:

$\frac{(2+x)(x-7)}{(x-5)(x+4)}=1$

The solution to the equation is x=3 or x=5/2.

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