Isn't there a way to solve this
(x+7)(x-1)= (x+1)(x+1)
like, making both sides have the same denominator ?
I know how to solve it the other way
Neither side has a denominator. There is no division indicated.
Multiply both sides out, combine like terms and then deal with that equation made to equal zero.
?x^2 ± ?x ± ? = 0
? = missing numerical values.
Is that what you did?
Factor that to solve.
To solve the equation (x+7)(x-1) = (x+1)(x+1), we can expand both sides of the equation and simplify it.
First, let's expand both sides:
(x+7)(x-1) = (x+1)(x+1)
x(x-1) + 7(x-1) = (x+1)(x+1)
x^2 - x + 7x - 7 = x^2 + 2x + 1
Now, we can simplify both sides:
x^2 + 6x - 7 = x^2 + 2x + 1
To make it easier to solve, we can move all terms to one side of the equation:
x^2 + 6x - 7 - x^2 - 2x - 1 = 0
4x - 8 = 0
Next, we can solve for x by isolating the variable:
4x - 8 = 0
4x = 8
x = 8/4
x = 2
Therefore, the solution to the equation (x+7)(x-1) = (x+1)(x+1) is x = 2.
Using a common denominator approach, as you mentioned, can be done as well. However, for this particular equation, it might not simplify the process significantly. Nevertheless, let's explore that method too:
(x+7)(x-1) = (x+1)(x+1)
Expand both sides:
x(x-1) + 7(x-1) = (x+1)(x+1)
x^2 - x + 7x - 7 = x^2 + 2x + 1
Combine like terms:
x^2 + 6x - 7 = x^2 + 2x + 1
Subtracting x^2 from both sides:
6x - 7 = 2x + 1
Subtracting 2x from both sides:
4x - 7 = 1
Adding 7 to both sides:
4x = 8
Dividing by 4:
x = 2
So the solution to the equation (x+7)(x-1) = (x+1)(x+1) is x = 2.