# Basic Algebra

Section 5.1

#22 Write fraction in simplest form. (-10a^3b^2c^3)/(15ab^4)

*I got the answer -(2a^2c^2)/(3 b^2), is this correct?

#48 Write the expression in simplest form. (ab-3a+5b-15)/(15+3a^2-5b-a^2b)

*I got the answer of -(a+b)(5+a^2), is this correct?

Section 5.2

#14 Multiply the fractions. (x^2-3x-10)/5x times (15x^2)/(3x-15)

*I got 5x^2+10x or 5x(x+2), which is correct?

#36 Divide the following fractions: 16x/(4x^2-16) divided by (4x-24)/(x^2-4x-12)

*I got x/x-2, is this correct?

#48. Perform the indicated operations. (14x-7)/(x^2+3x-4) times (x^2+6x+8)/(2x^2+5x-3) divided by (x^2+2x)/(x^2+2x-3)

*I got 7/x, is this correct?

Section 5.3

#22 Subtract. Express the results in simplest form. 5a/a-3 minus 15/a-3

#42 Add. Express results in simplest form. -12/(x^2+x-12) plus x^2/(x+3)*(x+4) plus x/(x^2+x-12)

Section 5.4

#56 Add. Express results in simplest form. 2/(3b-6)plus 3/(4b+8)

#72 Number problem. One number is two less than another. Use a rational expression to represent the sum of the reciprocals of the two numbers.

Section 5.5

#10 What values for x, if any, must be excluded in the following algebraic function: x-1/x-5

#32 Solve and check the following equations for x: 3/x = 5/3 minus 7/x

#54 Solve and check the following equations for x. 2/(x+2) = 3/(x+6) plus 9/(x^2+8x+12)

#70 Solve for x. x/10 = 9/30

Section 5.6

#8 Number problem. One number is 3 times another. If the sum of their reciprocals is 1/6, find the two numbers.

#16 Science and medicine. Tina can run 12 mi in the same time it takes her to bicycle 72 mi. If her bicycling rate is 20mi/h faster than her running rate, find each rate.

Section 5.7

#8 Simplify the comples fraction: 6/(x^2)/9/(x^3)

#28 Science and medicine. Fungicides account for 1/10 of the pesticides used in the US. Insecticides are 1/4 of all persticides used in the US. The ratio of fungicides to insecticides in the US can be written as 1/10 divided by 1/4. Write this ratio in simplest form.

#30 The area of a rectangle is 2(3x-2)/x-1. One of the long sides of the rectangle is (3x-2)/x-2. Find the width of the rectangle.

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#### Solution Summary

It shows how to solve various basic algebra questions. The solution is detailed and was rated '5/5' by the student who posted the questions originally.