Algebra II : Solving Rational Expressions

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #31 :Solving Rational Expressions

Solve for.

Possible Answers:

有限公司rrect answer:

Explanation:

To solve for the variable isolate it on one side of the equation by moving all other constants to the other side. To do this, perform opposite operations to manipulate the equation.

Cross multiply.

Remember we are multiplyingwith the expression. Now distribute.

Addon both sides.

Divideon both sides.

Example Question #32 :Solving Rational Expressions

Solve for.

Possible Answers:

有限公司rrect answer:

Explanation:

To solve for the variable isolate it on one side of the equation by moving all other constants to the other side. To do this, perform opposite operations to manipulate the equation.

Cross multiply.

Remember we are multiplyingto the expression. Now distribute.

Addon both sides.

Divideon both sides.

Example Question #33 :Solving Rational Expressions

Solve for.

Possible Answers:

有限公司rrect answer:

Explanation:

To solve for the variable isolate it on one side of the equation by moving all other constants to the other side. To do this, perform opposite operations to manipulate the equation.

Cross multiply.

Remember to multiply每一个表情。然后distribute.

Subtractandon both sides.

Example Question #34 :Solving Rational Expressions

Solve for.

Possible Answers:

有限公司rrect answer:

Explanation:

To solve for the variable isolate it on one side of the equation by moving all other constants to the other side. To do this, perform opposite operations to manipulate the equation.

Cross multiply.

Remember we are multiplyingto the expressions respectively. Then distribute.

Subtractandon both sides.

Example Question #35 :Solving Rational Expressions

Solve for.

Possible Answers:

有限公司rrect answer:

Explanation:

To solve for the variable isolate it on one side of the equation by moving all other constants to the other side. To do this, perform opposite operations to manipulate the equation.

Cross multiply.

Remember we are multiplyingto the expression. Then we distribute.

Subtracton both sides.

Divideon both sides.

Example Question #36 :Solving Rational Expressions

Solve for.

Possible Answers:

有限公司rrect answer:

Explanation:

To solve for the variable isolate it on one side of the equation by moving all other constants to the other side. To do this, perform opposite operations to manipulate the equation.

Distribute. Remember to apply FOIL.

Subtract,, andon both sides.

Divideon both sides.

Example Question #37 :Solving Rational Expressions

Simplify:

Possible Answers:

有限公司rrect answer:

Explanation:

To simplify the expressions, we will need a least common denominator.

Multiply the two denominators together to obtain the least common denominator.

有限公司nvert the fractions.

有限公司mbine the fractions as one fraction.

Simplify the numerator and combine like-terms.

The answer is:

Example Question #38 :Solving Rational Expressions

Possible Answers:

有限公司rrect answer:

Explanation:

When considering the solution space for a rational function, we must look at the denominator.

Any value of x in the denominator that results in a zero cannot be part of the solution space because it is a mathematical impossibility to divide by 0.

(add 16 to both sides)

(take the square root of both sides)

If we were to plug in a positive or negative 4 into the function, both of these would result in a zero in the denominator, which is a mathematical impossibility.

Example Question #701 :Intermediate Single Variable Algebra

Solve:

Possible Answers:

有限公司rrect answer:

Explanation:

有限公司nvert the fractions to a common denominator.

Simplify the top and bottom and combine like terms on the numerator.

The answer is:

Example Question #702 :Intermediate Single Variable Algebra

Solve:

Possible Answers:

有限公司rrect answer:

Explanation:

Find the least common denominator by multiplying both denominators together.

有限公司nvert the fractions.

Simplify the numerator and denominator.

有限公司mbine both fractions together. Remember to brace the second numerator in parentheses.

Simplify the fraction.

Factor out a negative one in the denominator.

The answer is:

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