I need help with this problem:
6/v-1=6/(v-3)
I tried working it out like this:
>>>6/v-1=6/(v-3)
>>>(6-v)/v= 6/(v-3)
I cross multiplied to get:
>>>3v+18-v^2= 6v
>>> -3v+18-v^2=0
^Here's where I became stuck. I would appreciate it if you would point out where I have gone wrong in this problem.
6/v-1=6/(v-3)
cross-multiply from here
6(v-3) = 6(v-1)
6v - 18 =6v - 6
-18 = -6
contradiction!
so your equation has no solution.
did you type it correctly?
The first step is wrong. How did you get (6-v)/v?
@Reiny: It is 6/v -1= 6/(v+3) I made a mistake there.
@bobpursley: From the 6/v-1 I made it one fraction
6/v -1/1 --> (6 -(1*v))/v
ok, multiply each term by v(v-3)
6(v-3) -v(v-3) = 6v
6v - 18 - v^2 + 3v = 6v
v^2 - 3v + 18 = 0
use the quadratic equation, but just looking at it, I can see that you will not get a real answer.
Your two roots will be complex numbers
To solve the equation 6/v-1 = 6/(v-3), let's go step by step and point out where you went wrong.
1. Start with the given equation: 6/v - 1 = 6/(v - 3).
2. To remove the fractions, you can multiply both sides of the equation by the least common multiple (LCM) of the denominators, which is v(v - 3).
Multiply both sides by v(v - 3):
v(v - 3) * (6/v - 1) = v(v - 3) * (6/(v - 3)).
After simplifying, the equation becomes:
6(v - 3) - v(v - 3) = 6v.
Expanding the brackets:
6v - 18 - v^2 + 3v = 6v.
Combining like terms:
9v - 18 - v^2 = 6v.
Rearranging the terms:
-v^2 + 3v - 18 = 6v.
Bringing all terms to one side:
-v^2 + 3v - 18 - 6v = 0.
Simplifying further:
-v^2 - 3v - 18 = 0.
Now, we can solve this quadratic equation: -v^2 - 3v - 18 = 0.
To solve a quadratic equation, there are a few methods, such as factoring, completing the square, or using the quadratic formula. In this case, let's solve it by factoring.
To factor -v^2 - 3v - 18 = 0, you need to find two numbers whose product is -18 and whose sum is -3.
The numbers -6 and 3 fit these conditions because -6 * 3 = -18 and -6 + 3 = -3.
We can rewrite the equation as:
(-v^2 - 6v) + (3v - 18) = 0.
Now, we factor by grouping:
v(-v - 6) + 3(v - 6) = 0.
(v - 6)(-v + 3) = 0.
Now, equating each factor to zero:
v - 6 = 0 --> v = 6,
and
-v + 3 = 0 --> v = 3.
So, the solution to the equation 6/v-1 = 6/(v-3) is v = 6 or v = 3.