solve each equation and check the result
7 3 40
x-5 - x+5 = x^2 - 25
there is a line in between each equation
how would i start something like this?
Surely there is an explanation, it makes no sense to me.
its solving rational equations
7 3 40
- - - = -
x-5 x+5 x^2-25
sorry i don't know how else to put the equation on the forum
Is this
7/(x-5) - 3/(x+5) = 40/(x^2-25) ?
If so get a common denominator (x^2-25) so it becomes
7(x+5)-3(x-5)=40
and one can solve that. Otherwise, I can make no sense from your problem.
yes that is it thank you
To solve the given equation, start by simplifying both sides of the equation.
The equation is:
(x - 5) - (x + 5) = x^2 - 25
On the left side of the equation, apply the distributive property to remove the parentheses:
x - 5 - x - 5 = x^2 - 25
Combine like terms:
-10 = x^2 - 25
Now, rearrange the terms to have the equation in standard form:
x^2 = -10 + 25
x^2 = 15
Next, take the square root of both sides of the equation. Remember to consider both positive and negative roots:
x = ±√15
So the two potential solutions are x = √15 and x = -√15.
To check if these solutions are correct, substitute them back into the original equation and verify if both sides of the equation are equal.
For x = √15:
Left side of the equation:
(√15 - 5) - (√15 + 5) = (√15 - √15) + (-5 - 5) = -10
Right side of the equation:
(√15)^2 - 25 = 15 - 25 = -10
Both sides of the equation are equal (-10 = -10), so x = √15 is a valid solution.
For x = -√15:
Left side of the equation:
(-√15 - 5) - (-√15 + 5) = (-√15 + √15) + (-5 - 5) = -10
Right side of the equation:
(-√15)^2 - 25 = 15 - 25 = -10
Both sides of the equation are equal (-10 = -10), so x = -√15 is also a valid solution.
Therefore, the solutions to the equation are x = √15 and x = -√15.