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May 25th, 2015

(5x^7/7-x) / (7x-1/49-x^2)

`Raise  x to the  2nd power`
```       (x7)   x      1
(((5•————)-(—•x))-——)-x2
7     7     49
```
```           x
Multiply  —  by  x
7
```

#### x1 multiplied by x1 = x(1 + 1) = x2

```       (x7)  x2   1
(((5•————)-——)-——)-x2
7    7   49
```
``` Raise  x to the  7th power
```
```         x7     x2      1
(((5 • ——) -  ——) -  ——) -  x2
7      7      49
```
```           5x7     x2
Simplify   ———  -  ——
7      7 ```

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

``` 5x7 - (x2)     5x7 - x2
——————————  =  ————————
7             7
```
```   (5x7 - x2)     1
(—————————— -  ——) -  x2
7         49
```
```           5x7-x2      1
Simplify   ——————  -  ——
7        49
```

#### Pull out like factors :

5x7 - x2 =  x2 • (5x5 - 1)

#### Find the Least Common Multiple

Least Common Multiple:
49

#### Rewrite the two fractions into equivalent fractions

```   L. Mult. • L. Num.      x2 • (5x5-1) • 7
——————————————————  =   ————————————————
L.C.M                    49

R. Mult. • R. Num.       1
——————————————————  =   ——
L.C.M             49```

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

``` x2 • (5x5-1) • 7 - (1)     35x7 - 7x2 - 1
——————————————————————  =  ——————————————
49                     49
```
```  (35x7 - 7x2 - 1)
———————————————— -  x2
49           ```
```           35x7-7x2-1
Simplify   ——————————  -  x2
49         ```

Rewrite the whole as a fraction using  49  as the denominator :

```           x2     x2 • 49
x2 =  ——  =  ———————
1        49   ```
``` (35x7-7x2-1) - (x2 • 49)      35x7 - 56x2 - 1
————————————————————————  =  ———————————————
49                      49
```

```  35x7 - 56x2 - 1
———————————————
49       ```

May 26th, 2015

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May 25th, 2015
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May 25th, 2015
Sep 26th, 2017
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