(x%2B2)%2F(x%2B11)(x-2)%3D1.jpeg "(x+1)(x+2)/(x+11)(x-2)=1")
Solving the Equation: (x+1)(x+2)/(x+11)(x-2)=1
In this article, we will explore the solution to the equation:
$\frac{(x+1)(x+2)}{(x+11)(x-2)}=1$
This equation involves the multiplication of binomials and the use of algebraic properties to solve for x.
Step 1: Multiply the Binomials
To begin, let's multiply the binomials in the numerator:
$(x+1)(x+2) = x^2 + 3x + 2$
Step 2: Rewrite the Equation
Now, let's rewrite the original equation with the multiplied binomials:
$\frac{x^2 + 3x + 2}{(x+11)(x-2)}=1$
Step 3: Cross-Multiply
Next, we can cross-multiply to eliminate the fraction:
$x^2 + 3x + 2 = (x+11)(x-2)$
Step 4: Expand and Simplify
Expanding the right-hand side of the equation, we get:
$x^2 + 3x + 2 = x^2 + 9x - 22$
Step 5: Solve for x
Now, let's solve for x by moving all terms to one side of the equation:
$3x - 24 = 0$
Dividing both sides by 3, we get:
$x = 8$
Therefore, the solution to the equation is x = 8.
In conclusion, by using algebraic properties and following the steps outlined above, we were able to solve for x in the equation:
$\frac{(x+1)(x+2)}{(x+11)(x-2)}=1$
with the solution x = 8.
