Choose the statement that is not true. Assume b ≠0, c ≠0, and d ≠0 as necessary. (a) (a c)/(b

step 1 When trying to see which of these four equations is incorrect, we start with number one, and we

Choose the statement that is not true. Assume b ≠0, c ≠0,...

Choose the statement that is not true. Assume $b \neq 0, c \neq 0$, and $d \neq 0$ as necessary. $$ \text { (a) } \frac{a c}{b c}=\frac{a}{b} \quad \text { (b) } \frac{a}{b}+\frac{c}{b}=\frac{a+c}{b} $$ $$ \text { (c) } \frac{a}{b}-\frac{c}{d}=\frac{a d-b c}{b d} \quad \text { (d) } \frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a c}{b d} $$

Choose the statement that is not true. Assume $b \neq 0, c \neq 0$, and $d \neq 0$ as necessary.
$$
\text { (a) } \frac{a c}{b c}=\frac{a}{b} \quad \text { (b) } \frac{a}{b}+\frac{c}{b}=\frac{a+c}{b}
$$
$$
\text { (c) } \frac{a}{b}-\frac{c}{d}=\frac{a d-b c}{b d} \quad \text { (d) } \frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a c}{b d}
$$

Key Concepts

Simplification of Algebraic Fractions

This concept involves canceling common nonzero factors from the numerator and denominator of a fraction. When factors are canceled, it reduces the expression to a simpler, equivalent form. It is essential to recognize that cancellation is valid only when the factors in question are nonzero, which is why it is stipulated in many problems that certain variables are not equal to zero.

Addition of Algebraic Fractions

Adding fractions with the same denominator can be done by simply adding their numerators while keeping the common denominator unchanged. This concept is crucial for handling algebraic expressions and ensures that the addition process is straightforward when the denominators are identical.

Subtraction of Algebraic Fractions

Subtraction of fractions, like addition, requires a common denominator to combine the fractions into a single expression. When the denominators differ, a common denominator must be found, and the numerators adjusted accordingly before performing the subtraction. This concept underpins the correct manipulation of differences in algebraic fractions.

Division of Algebraic Fractions

Dividing one algebraic fraction by another involves multiplying by the reciprocal of the divisor. This transformation leverages the multiplication of fractions, where numerators and denominators are multiplied respectively. Recognizing the need to take the reciprocal is key to correctly performing division of fractions.

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