All Algebra II Resources
Example Question #1 : Solving Rational Expressions
Solve for :
To solve this rational equation, start by cross multiplying:
Then, distribute the right side:
Finally, subtract from both sides and bring the over to the left side:
Dividing by gives the answer:
Example Question #2 : Solving Rational Expressions
Solve for :
The first step is to multiply everything by a common denominator. One way to do this is to multiply the entire equation by all three denominators:
Then, to solve for , use the quadratic formula:
Example Question #3 : Solving Rational Expressions
Solve for , given the equation below.
Begin by cross-multiplying.
Distribute the on the left side and expand the polynomial on the right.
Combine like terms and rearrange to set the equation equal to zero.
Now we can isolate and solve for by adding to both sides.
Example Question #4 : Solving Rational Expressions
Solve the rational equation:
With rational equations we must first note the domain, which is all real numbers except and . That is, these are the values of that will cause the equation to be undefined. Since the least common denominator of , , and is , we can mulitply each term by the LCD to cancel out the denominators and reduce the equation to . Combining like terms, we end up with . Dividing both sides of the equation by the constant, we obtain an answer of . However, this solution is NOT in the domain. Thus, there is NO SOLUTION because is an extraneous answer.
Example Question #5 : Solving Rational Expressions
Factor out from the numerator which gives us
Hence we get the following
which is equal to
Example Question #4 : How To Subtract Polynomials
First we convert each of the denominators into an LCD which gives us the following:
Now we add or subtract the numerators which gives us:
Simplifying the above equation gives us the answer which is:
Example Question #6 : Solving Rational Expressions
Solve for .
The two fractions on the left side of the equation need a common denominator. We can easily do find one by multiplying both the top and bottom of each fraction by the denominator of the other.
Now add the two fractions:
To solve, multiply both sides of the equation by , yielding
Multiply both sides by 3:
Move all terms to the same side:
This looks like a complicated equation to factor, but luckily, the only factors of 37 are 37 and 1, so we are left with
Our solutions are therefore
Example Question #4 : How To Find The Solution To A Rational Equation With Lcd
Solve for :
Multiply both sides by :
Factor this using the -method. We split the middle term using two integers whose sum is and whose product is . These integers are :
Set each factor equal to 0 and solve separately:
Example Question #7 : Solving Rational Expressions
Simplify the following expression:
This expression is already simplified.
The first step of problems like this is to try to factor the quadratic and see if it shares a factor with the linear polynomial in the denominator. And as it turns out,
So our rational function is equal to
which is as simplified as it can get.
Example Question #8 : Solving Rational Expressions
Evaluate the following expression:
You cannot divide fractions.
When dividing fractions, we multiply by the reciprocal of the second fraction. Therefore, the problem becomes:
Our final unfactored expression is therefore .