4/v = v-6/v-4? Help with Math...?

Question

What is the answer to 4/V = V-6/V-4? I am suppose to solve using the Quadratic Formula, but I have no idea how to do this...

Answer 1

Is it 4/V = (V - 6)/(V - 4)?

Then multiply both sides by the product of the denominators V*(V-4) to get

4*(V-4) = V*(V-6)

Multiply out each side to get

4*V - 16 = V^2 - 6*V

Rearrange terms to get

V^2 - 10*V +16 = 0

Now you have your quadratic equation which you should be able to solve

Answer 2

4/v = (v - 6)/(v - 4)

First, if it is given that you use the quadratic formula, then that must be a quadratic equation. A quadratic equation is any equation in the form
ax² + bx + c = 0
where a,b and c are all real number constant.

Examples:
3x² + 4x + 1 = 0 is an example of a quadratic equation
-22x² + 1000x - 23 = 0 is also a quadratic equation
30t² - 11t - 3 = 0 is also a quadratic equation
33x² - 2 = 0 is also a quadratic equation (note that here, b = 0)

Now it doesn't seem to be a quadratic now, but you can transform the equation into one by using algebra.
4/v = (v - 6)/(v - 4)

It is very hard to work with fractions involving variables, so here you can cross-multiply
4(v - 4) = v(v - 6)

Distribute
4v - 16 = v² - 6v

Now you can transpose everything to the left, leaving a 0 on the right side
4v - 16 - v² + 6v = 0

Add like terms
-v² + 10v - 16 = 0

Multiply -1
v² - 10v + 16 = 0

Now you can see that it is now a quadratic equation. There is a method of solving this kind of equation which is the Quadratic Formula, which you can now use, but if you do not know it, then here it is.

The Quadratic Formula

If you have the quadratic equation
ax² + bx + c = 0, where a, b and c are all real number constants,
then the solution for the variable x is
x = [-b ± √(b² - 4ac)]/2a


Since your equation is
v² - 10v + 16 = 0,
compare it to
ax² + bx + c = 0
and you get
v = x
a = 1
b = -10
c = 16

You can now substitute the values and solve for v.
x = [-b ± √(b² - 4ac)]/2a
v = [-(-10) ± √{(-10)² - 4(1)(16)}]/2(1)
v = [10 ± √(100 - 64)]/2
v = [10 ± √(36)]/2
v = (10 ± 6)/2

Thus,
v = (10 + 6)/2 or v = (10 - 6)/2
v = 16/2 or v = 4/2
v = 8 or v = 2

^_^

Answer 3

Cross multiply.
4(v-4) = (v-6)v
4v - 16 = v^2 - 6v
Move everything to one side by subtracting 4v and adding 16 to each side.
0 = v^2 - 10v + 16
Now factor.
What factors of 16 add to -10?
-8(-2) = 16 and -8 - 2 = -10
0 = (v-8)(v-2)
v - 8 = 0 or v - 2 = 0
v = 8 or v = 2
You should always check your answer because with this type of equation, sometimes your "solutions" do not work.

Answer 4

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Answer 5

first cross multiply

4(v-4_= v(v-6)
4v-16 = v2 - 6v
0r
-16 = V2 -6V-4V
=> V2 -10V = -16
=> V2 - 10V +16 = 0
Solving the quadratic equation(-8X-2 = 16, -8+(-2) = -10)
(v-8)(v-2) = 0 i.e (v-8) = 0 or v-2 = 0
v=8 or v= 2

Hope it is clear

Answer 6

(4/v) = (v - 6)/(v - 4)

cross multiply

v(v - 6) = 4(v - 4)
v^2 - 6v = 4v - 16
v^2 - 10v + 16 = 0
(v - 8)(v - 2) = 0

v = 8 or 2

Answer 7

Just set everything equal to "V" by multiplying the whole equation by "4"