Simplify these expressions?

Dear Ed,

rtx*(3x+1)

Multiply rtx by each term inside the parentheses.

(3rtx^(2)+rtx)

Remove the parentheses around the expression 3rtx^(2)+rtx.

3rtx^(2)+rtx

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((x-1)^(2))/(2x*rtx)

Multiply 2x by rtx to get 2rtx^(2).

((x-1)^(2))/(2rtx^(2))

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(a^(-1)*b+b^(-2))/(ab^(2)+b^(-1))

Remove the negative exponent in the numerator by rewriting a^(-1) as (1)/(a). A negative exponent follows the rule: a^(-n)=(1)/(a^(n)).

((1)/(a)*b+b^(-2))/(ab^(2)+b^(-1))

Remove the negative exponent in the numerator by rewriting b^(-2) as (1)/(b^(2)). A negative exponent follows the rule: a^(-n)=(1)/(a^(n)).

((1)/(a)*b+(1)/(b^(2)))/(ab^(2)+b^(-1))

Multiply (1)/(a) by b to get (b)/(a).

((b)/(a)+(1)/(b^(2)))/(ab^(2)+b^(-1))

To add fractions, the denominators must be equal. The denominators can be made equal by finding the least common denominator (LCD). In this case, the LCD is ab^(2). Next, multiply each fraction by a factor of 1 that will create the LCD in each of the fractions.

((b)/(a)*(b^(2))/(b^(2))+(1)/(b^(2))*(a)/(a))/(ab^(2)+b^(-1))

Complete the multiplication to produce a denominator of ab^(2) in each expression.

((b^(3))/(ab^(2))+(a)/(ab^(2)))/(ab^(2)+b^(-1))

Combine the numerators of all expressions that have common denominators.

(((b^(3)+a)/(ab^(2))))/(ab^(2)+b^(-1))

Remove the negative exponent in the numerator by rewriting b^(-1) as (1)/(b). A negative exponent follows the rule: a^(-n)=(1)/(a^(n)).

(((b^(3)+a)/(ab^(2))))/(ab^(2)+(1)/(b))

To add fractions, the denominators must be equal. The denominators can be made equal by finding the least common denominator (LCD). In this case, the LCD is b. Next, multiply each fraction by a factor of 1 that will create the LCD in each of the fractions.

(((b^(3)+a)/(ab^(2))))/(ab^(2)*(b)/(b)+(1)/(b))

Complete the multiplication to produce a denominator of b in each expression.

(((b^(3)+a)/(ab^(2))))/((ab^(3))/(b)+(1)/(b))

Combine the numerators of all expressions that have common denominators.

(((b^(3)+a)/(ab^(2))))/((ab^(3)+1)/(b))

To divide by ((ab^(3)+1))/(b), multiply by the reciprocal of the fraction.

(b)/(ab^(3)+1)*(b^(3)+a)/(ab^(2))

Remove the common factor of b from the numerator of the first expression and denominator of the second expression.

(1)/(ab^(3)+1)*(b^(3)+a)/(ba)

Arrange the variables alphabetically within the expression ba. This is the standard way of writing an expression.

(b^(3)+a)/((ab)(ab^(3)+1))

Remove the parentheses around the ab in the denominator.

(b^(3)+a)/(ab(ab^(3)+1))