"How to Solve a Linear Equation that has Fractions"

Solve the linear equation 

`2(x+5)/(x-1) = 3` 

First,  clear the fraction by multiplying both sides of the equation by `(x-1)`. This gives us `2(x+5) = 3(x-1)`. 

Next,  distribute the `2` and `3` on both sides of the equation to get `2x + 10 = 3x - 3`. You have simply removed the brackets from both sides.

Now,  isolate the variable `x` on one side of the equation by subtracting `2x` from both sides. This gives us `10 = x - 3`. 

Finally, we can solve for `x` by adding `3` to both sides of the equation. This gives us `x = 13`.

So, the solution to the linear equation `2(x+5)/(x-1) = 3` is `x = 13`.

Here's another example: Let's solve the linear equation `(x+2)/(x-3) = 4`. 

First,  clear the fraction by multiplying both sides of the equation by `(x-3)`. This gives us `x + 2 = 4(x-3)`.

Next, distribute the `4` on the right side of the equation to get `x + 2 = 4x - 12`.

Now,  isolate the variable `x` on one side of the equation by subtracting `x` from both sides. This gives us `2 = 3x - 12`.

Finally, you can solve for `x` by adding `12` to both sides of the equation and then dividing both sides by `3`. This gives us `x = (2 + 12)/3`, which simplifies to `x = 14/3`.

So, the solution to the linear equation `(x+2)/(x-3) = 4` is `x = 14/3`.

In conclusion, solving linear equations involves isolating the variable on one side of the equation and performing operations on both sides of the equation to simplify it.

Here are three practice exercises for you to try:

1. Solve `(2x + 1)/(x - 4) = 5`.

2. Solve `(3 - x)/(2x + 1) = -1`.

3. Solve `(4 - x)/(5 + x) = -1/2`.

This article was written by Awah Aweh who is an experience Math teacher and a Marketing content and copy writer.