Algebra II : Simplifying Equations

Example Questions

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Example Question #11 : Simplifying Equations

Simplify:

Explanation:

To simplify the equation you need to divide the numerator (top) and denominator (bottom), so:

The numerator can be factored to:

The  denominator can be factored to:

After reducing, we will get

Example Question #12 : Simplifying Equations

Simplify:

Explanation:

To simplify the equation you need to divide the numerator (top) and denominator (bottom), so:

The numerator can be factored to:

The  denominator can be factored to:

After reducing, we will get

Example Question #13 : Simplifying Equations

Solve for :

Explanation:

Multiply  on both sides in order to eliminate the denominator.

Simplify both sides.

Use distribution to simplify both sides.

Isolate the term with only the y-variable by subtracting  on both sides.

Simplify and reorder the right side by the order of power.

Divide by  on both sides.

Simplify both sides.

Example Question #14 : Simplifying Equations

Simplify the equation:

Explanation:

In order to simplify and solve this equation, divide by six on both sides.

Simplify both sides.

Simplify both sides.

Divide both sides by two.

Example Question #15 : Simplifying Equations

Simplify the following equation:

Explanation:

Subtract nine from both sides.

Divide both sides.

Example Question #16 : Simplifying Equations

Simplify the equation:

Explanation:

Divide by two on both sides.

The equation becomes:

Divide by three on both sides.

Example Question #17 : Simplifying Equations

Simplify the equation:

Explanation:

Start by squaring everything within the parentheses:

Now combine the fractions of degree 1 by finding a common denominator:

Example Question #18 : Simplifying Equations

Simplify this expression:

Explanation:

Drop the parentheses and combine like terms.

and

Example Question #19 : Simplifying Equations

Simplify the expression by combining like terms.

Simplify:

Explanation:

The original equation:

Now move all terms to one side, in this example, we will use the right side, but either side will work.

As you can see, we subtracted the terms on the left from both sides, effectively moving them to the other side.

Regrouping the terms so that "like terms" are together. Like terms are defined by having the same power of x.

Now, we add any terms that have like powers of x.

Now that all terms have been combined, we are finished. The equation is simplified.

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