Solve. For Exercises 83 and 84, see the second Concept Check...

Solve. For Exercises 83 and $84,$ see the second Concept Check in this section, for Exercises 85 and $86,$ see the third Concept Check. A parallelogram has an area of $\frac{x^{2}+x-2}{x^{3}}$ square feet and a height of $\frac{x^{2}}{x-1}$ feet. Express the length of its base as a rational expression in $x .$ (Hint: since $A=b \cdot h, b=\frac{A}{h}$ or $b=A \div h .)$ (IMAGE CANNOT COPY)

Solve. For Exercises 83 and $84,$ see the second Concept Check in this section, for Exercises 85 and $86,$ see the third Concept Check.
A parallelogram has an area of $\frac{x^{2}+x-2}{x^{3}}$ square feet and a height of $\frac{x^{2}}{x-1}$ feet. Express the length of its base as a rational expression in $x .$ (Hint: since $A=b \cdot h, b=\frac{A}{h}$ or $b=A \div h .)$
(IMAGE CANNOT COPY)

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Key Concepts

Parallelogram Area Formula

The area of a parallelogram is given by multiplying its base by its height. This fundamental geometric formula, A = b · h, allows one to relate the dimensions of a parallelogram. It is often used to find one of the dimensions when the area and the other dimension are known.

Rational Expressions and Operations

Rational expressions are fractions where the numerator and the denominator are polynomials. Understanding how to work with rational expressions is essential, especially in problems that involve division and multiplication of polynomials, as these expressions often require simplifying by factoring and canceling common factors.

Division of Algebraic Fractions

Dividing algebraic fractions involves multiplying by the reciprocal of the divisor. This operation is central when solving problems where one rational expression is divided by another. Mastery of this technique is necessary to simplify complex algebraic fractions and solve equations that contain them.

Factoring Polynomials

Factoring is a technique used to simplify algebraic expressions by breaking them down into products of simpler polynomials. It is particularly useful in simplifying rational expressions and finding common factors in numerators and denominators, which can then be canceled to reduce the expression.

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