Chapter 7.4, Problem 3OE

To determine

To calculate: The result of the equations and the L.C.M

  $\frac{4}{y}-\frac{1}{4}=\frac{1}{12}$ .

Answer to Problem 3OE

The results of the equations is $y=12$ and the L.C.M is $4y$ .

Explanation of Solution

Given information:

The equation is $\frac{4}{y}-\frac{1}{4}=\frac{1}{12}$ .

Formula used:

We will take the L.C.M of the denominator.

And then we take like term to right hand side and variable term to left hand side.

Calculation:

Consider the equation.

  $\frac{4}{y}-\frac{1}{4}=\frac{1}{12}$ .

Now, in the above equation we have $y$ has variable .

Recall that we will take the L.C.M of the denominator.

Therefore L.C.M of $\left(y,4\right)=4y$ .

Recall that we take like term to right hand side and variable term to left hand side.

Now we will multiply the L.C.M from each term of the equation above.

Therefore $4y*\left(\frac{4}{y}\right)-4y*\left(\frac{1}{4}\right)=4y*\frac{1}{12}$ .

We gained that $16-y=\frac{y}{3}\mathrm{............}\left(i\right)$ .

We multiply $3$ both side of the equation $\left(i\right)$ .

Then $48-3y=y$ $\Rightarrow 48=4y\Rightarrow y=12$ .

Therefore the results of the equations is $y=12$ and the L.C.M is $4y$ .