# Find The Value Of The Variable y

Find The Value Of The Variable y

$Find The Value Of The Variable y$

## This Post Has 12 Comments

1. crun says:

y = 12

Step-by-step explanation:

Ordinarily, in math, when we say "the difference between ..." we mean the second listed item is subtracted from the first. (In English, we often mean "the positive difference between ..." so the order doesn't matter.)

We'll assume we are only interested in the case where the difference is in the order listed.

$\dfrac{y+12}{y-4}-\dfrac{y}{y+4}=\dfrac{y+12}{y-4}\cdot\dfrac{y}{y+4}\\\\\dfrac{(y+12)(y+4)-(y-4)(y)}{y^2-16}=\dfrac{(y+12)(y)}{y^2-16}\\\\0=\dfrac{y^2-8y-48}{y^2-16}=\dfrac{(y-12)(y+4)}{(y-4)(y+4)}=\dfrac{y-12}{y-4}\qquad\text{y\ne -4}\\\\\boxed{y=12}$

There is one solution.

_____

Comment on the solution

If you were to "clear fractions" by multiplying the equation by (y^2-16), you would also obtain the extraneous solution y=-4. That is why we did not solve it that way.

2. mmcdaniels46867 says:

y = -11

Step-by-step explanation:

$\text{Sum:}\\\\.\quad \dfrac{y+1}{y-5}+\dfrac{10}{y+5}\\\\\\=\bigg(\dfrac{y+5}{y+5}\bigg)\dfrac{y+1}{y-5}+\dfrac{10}{y+5}\bigg(\dfrac{y-5}{y-5}\bigg)\\\\\\=\dfrac{y^2+6y+5}{(y+5)(y-5)}+\dfrac{10y-50}{(y+5)(y-5)}\\\\\\=\dfrac{y^2+6y+5+10y-50}{(y+5)(y-5)}\\\\\\=\dfrac{y^2+16y-45}{(y+5)(y-5)}$

$\text{Product:}\\\\.\quad \dfrac{(y+1)(10)}{(y-5)(y+5)}\\\\\\=\dfrac{10y+10}{(y-5)(y+5)}\\\\\\\text{Sum = Product:}\\\\\dfrac{y^2+16y-45}{(y+5)(y-5)}=\dfrac{10y+10}{(y+5)(y-5)}\qquad Restriction: y\neq -5, 5\\\\\\\rightarrow y^2+16y-45=10y+10\\\\\rightarrow y^2+6y-55=0\\\\\rightarrow (y+11)(y-5)=0\\\\\rightarrow y+11=0\quad and\quad y-5=0\\\\\rightarrow y=-11\qquad and\qquad y=5\\\\\\\text{Since y = 5 is a restricted value, it is not a valid solution}$

3. Expert says:

2

step-by-step explanation:

$What’s the answer me i’ll give you a cookie$

4. Expert says:

5. Dexter992 says:

$-5.7+y=8.2\qquad\text{add 5.7 to both sides}\\\\\boxed{y=13.9}\to\boxed{D.}$

6. zmirandalove100 says:

Y=12.8*2=25.6
y=25.6

7. clarawulf9477 says:

6

Step-by-step explanation:

$\text{Difference:}\\\\.\quad \dfrac{6}{y-4}-\dfrac{y}{y+2}\\\\\\=\bigg(\dfrac{y+2}{y+2}\bigg)\dfrac{6}{y-4}-\dfrac{y}{y+2}\bigg(\dfrac{y-4}{y-4}\bigg)\\\\\\=\dfrac{6y+12}{(y+2)(y-4)}-\dfrac{y^2-4y}{(y+2)(y-4)}\\\\\\=\dfrac{6y+12-(y^2-4y)}{(y+2)(y-4)}\\\\\\=\dfrac{-y^2+10y+12}{(y+2)(y-4)}$

$\text{Product:}\\\\.\quad \dfrac{(6)(y)}{(y-4)(y+2)}\\\\\\=\dfrac{6y}{(y-4)(y+2)}\\\\\\\text{Difference = Product:}\\\\\dfrac{-y^2+10y+12}{(y+2)(y-4)}=\dfrac{6y}{(y+2)(y-4)}\qquad Restriction: y\neq -2, 4\\\\\\\rightarrow -y^2+10y+12=6y\\\\\rightarrow 0=y^2-4y-12\\\\\rightarrow 0=(y-6)(y+2)\\\\\rightarrow 0=y-6\quad and\quad 0=y+2\\\\\rightarrow 6=y\qquad and\quad -2=y\\\\\text{Since y = -2 is a restricted value, it is not a valid solution}\\\text{So, y = 6}$

8. tatilynnsoto17 says:

Lewis–Randall rule or Lewis fugacity rule states that fugacity of a component in an ideal solution is directly proportional to the mole

fraction of the component in the solution.

39 A solution in which the partial molar volumes of the components are the same as their molar volumes in the pure state is called an

40 Henry’s law and Raoult’s law are identical when

9. 4300404440 says:

Set up:

6/(y - 4) - y/(y + 2) = (6/y - 4)(y/y + 2)

Take it from here. Solve for y.

10. babymiche829 says:

The value of the variable y is $y=6$

Explanation:

The given equation is $\frac{6}{y-4}-\frac{y}{y+2}=\left(\frac{6}{y-4}\right)\left(\frac{y}{y+2}\right)$

Taking LCM on LHS of the equation, we get,

$\frac{6(y+2)-y(y-4)}{(y-4)(y+2)}=\left(\frac{6}{y-4}\right)\left(\frac{y}{y+2}\right)$

Simplifying the term on RHS of the equation, we get,

$\frac{6(y+2)-y(y-4)}{(y-4)(y+2)}=\frac{6 y}{(y-4)(y+2)}$

Since, both the sides of the equation have the same denominator, we can cancel them.

Thus, we have,

$6(y+2)-y(y-4)=6 y$

Multiplying the terms within the bracket, we get,

$6y+12-y^2-4y=6 y$

Adding the like terms, we have,

$2y+12-y^2=6 y$

Subtracting both sides by $6 y$, we have,

$-4y+12-y^2=0$

Factoring the equation, we get,

$(y+2)(y-6)=0$

$y=-2, y=6$

The values of the variable y are $y=-2, y=6$

At the point $y=-2$, the equation $\frac{6}{y-4}-\frac{y}{y+2}=\left(\frac{6}{y-4}\right)\left(\frac{y}{y+2}\right)$ becomes undefined.

Thus, the value of the variable y is $y=6$

11. avaleasim says:

63 is [email protected]

Step-by-step explanation:

12. estefaniapenalo says:

y = 13.9

Step-by-step explanation:

It is given that

–5.7 + y = 8.2.    (1)

Equation (1) is a linear equation in one variable.

LHS consists of a constant and a variable term

RHS consists of only constant term

Find the value of y

Solving the equation

-5.7 + y = 8.2

moving -5.7 to the RHS

y = 8.2 + 5.7

y = 13.9

Therefore the value of y = 13.9

-5.7 + y = 8.2