v/3 +v/v+5 = -4/v+5
You need to use parenthesis. If this is your problem
v/(v+5)+v/3 = -4/(v+5)
Multiply both sides by 3(v+5)
3v + v(v + 5) = -12
3v + v^2 + 5v = 12
v^2 + 8v + 12 = 0
(v + 2)(v + 6)
v = -6 or v = -2
Make sure you check the solutions in the original equation.
I have NOT checked the answers.
x/x + 12 -1 = 1/2x
To solve the equation v/3 + v/(v+5) = -4/(v+5), we need to find the value(s) of v that make the equation true.
Step 1: Simplify the equation by finding a common denominator.
The common denominator for the fractions on the left side of the equation is (v+5)*3. Multiply both sides of the equation by this common denominator to eliminate the denominators:
(v+5)*3 * (v/3) + (v+5)*3 * (v/(v+5)) = -4/(v+5) * (v+5)*3
Simplifying further:
v(v+5) + 3v = -4 * 3
Expand and combine like terms:
v^2 + 5v + 3v = -12
v^2 + 8v = -12
Step 2: Rearrange the equation as a quadratic equation.
To solve for v, rearrange the equation to form a quadratic equation, setting it equal to zero:
v^2 + 8v + 12 = 0
Step 3: Solve the quadratic equation.
To solve the quadratic equation, you can either factor it or use the quadratic formula. Factoring the equation:
(v + 2)(v + 6) = 0
Setting each factor equal to zero:
v + 2 = 0 or v + 6 = 0
From these equations, we get:
v = -2 or v = -6
Therefore, the solutions for the original equation v/3 + v/(v+5) = -4/(v+5) are v = -2 and v = -6.