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Kasten, Algebra 2 Algebra Review

Complex Fractions

A complex fraction is an expression that features fractions within fractions. To simplify complex fractions, we only need to master one very simple method.

Example:

Simplify

76+38 4-34

Solution:

The trick is to multiply the numerator and denominator of the big fraction by the least common denominator of every little fraction.

The little fractions have denominators 6, 8, and 4. The LCM of 6, 8, and 4 is 24.

So, multiply the top and bottom by 24:

7 6

4

+ -

3 8 3 4

24 24

=

7 6

4

24 24

+ -

3 8 3 4

24 24

=

28 + 9 96 - 18

=

37 78

There really is nothing more to it. No matter how complicated the complex fractions may look, this method will work!

Just remember: If you are dealing with a variable in the denominator, be sure to note excluded values (values of the variable that would make the denominator zero).

Practice: simplify complex fractions

1-1 1. 12-12

(Note the excluded values 0 and 0)

Kasten, Algebra 2 Algebra Review

2

2.

2-9

+4 3+-43

(Factor (2 - 9), then find the LCD)

3.

4 +

3 2++1 3

Radical Equations

Kasten, Algebra 2 Algebra Review

A radical equation is an equation in which at least one variable is "stuck" inside of a radical sign (usually, a square root). For example: + 1 = 2

To solve radical equations, we isolate the variable (as usual).

Example: Solve + 1 = 2

Solution:

To "undo" the square root, square both sides of the equation (in other words, raise both sides of the equation to a power of 2):

(

+

2

1)

=

(2)2

We get:

+ 1 = 4

Then, subtract 1 from both sides of the equation:

+ 1 - 1 = 4 - 1

We get:

= 3

Kasten, Algebra 2 Algebra Review

In the previous example, the radical was isolated on the left-hand side to begin with. This is often not the case! If the radical is not isolated to begin with, don't jump straight to undoing the radical!

Example: Solve + 2 = 6

Solution:

We want to isolate . Start by subtracting 2 from both sides of the equation:

We get:

+ 2 - 2 = 6 - 2

= 4

Now, once we have the radical isolated, we can square both sides of the equation to undo the square root:

= 16

Kasten, Algebra 2 Algebra Review

Check your Solutions! Keep in mind that even roots (for example, , 4, 32, etc.) are always positive. Test makers like to set up false equations that, even if you perform all of your algebra correctly, will yield incorrect solutions!

Example:

Solve + 1 = -3

Solution:

Subtract 1 from both sides of the equation:

+ 1 - 1 = -3 - 1

We get:

= -4

*TRAP* If we were to square both sides, we would get = 16, but this answer is incorrect!

Once we see " = -4", we know there is actually no solution, since even roots are always positive!

Thus, the correct answer to this problem is: NO SOLUTION

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