Need help with Algebra Rational Equations and Rational Expressions?

Question

1) Find all numbers for which the rational expression is undefined .

4/v - 8

2.) Divide and simplify

c + 6/c - 7 / 2c + 12/c - 1

3.) Solve

z - 1/z - 4 = 3/z - 4

4.) Find the LCM of 7(x - 2) and 14(x - 2)

5.)Solve

x/x + 7 - 7/x - 7 = x^2 + 49/x^2 - 49

6.) Simplify by removing factors of 1.

48w^8 y^9/18w^4 y^3

7.) Add and simplify if possible

8t/t^2 - 9 + t/t - 3

8.) Find the LCM

v^3 + 8v^2 + 16v, v^2 - 8v

9.) Divide and simplify

x^2 + 9x/x^2 + 3x - 54 / x x + 6

10.) Simplify by removing factors of 1.

t^2 - 36/(t + 6)^2

11.) Subtract and simplify if possible

1/3s^2 - 3s - 5/3s - 3

12.) Simplify by removing factors of 1.

y^2 - 6y + 5/y^2 + 5y - 6

13.) Multiply and simplify

3x^3/7x^2 * 49x^4/9x

14.)Subtract and simplify if possible.

19/b - 5 - 19/5 - b

15.)Add and simplify if possible

3/4z^3 + 1/6z^2

16.)Solve

x + 8/x = -9

17.) Solve

8/z + 6 = 7/z + 5

18.) Add and simplify if possible

4b/5b - 10 + 9b/10b - 20

Someone please help me with these problems I am having a test on these and I am not sure on how to do them so anything anyone can do and show work so I will know how you got your answer I would greatly appreciate.

Answer 1

Here are a few.

1) Find all numbers for which the rational expression is undefined .

4/v - 8

You can't divide by zero.

Set the denominator equal to zero to find where the expression is undefined.

The denominator is just v, so v = 0 is where the expression is undefined.

If you meant 4/(v-8), then the denominator is v-8.

v-8 = 0 means v = 8, so the expression is undefined when v = 8.

I hope you see the DIFFERENCE between 4/v - 8 and 4/(v-8).

2.) Divide and simplify

c + 6/c - 7 / 2c + 12/c - 1

With no parentheses, your expression is difficult to interpret.

What are the denominators?  numerators?  

3.) Solve

z - 1/z - 4 = 3/z - 4

Again, you don't have parentheses, but I THINK you mean

(z-1)/(z-4) = 3/(z-4) ....... but I am not 100% sure.

You could also mean z - 1/(z-4) = 3/(z-4).

Or possibly something else.

I'll assume you mean (z-1)/(z-4) = 3/(z-4).

Since the denominators are equal, you can just drop them.

z - 1 = 3

Add 1 to each side.

z = 4

Then go back to the original equation to see if this solution makes sense.

If you plug in z=4, then you will be dividing by zero.  Therefore, there is no solution.

4.) Find the LCM of 7(x - 2) and 14(x - 2)

The LCM is 14(x-2).

5.)Solve

x/x + 7 - 7/x - 7 = x^2 + 49/x^2 - 49

Still no parentheses, but let's assume you mean

x/(x+7) - 7/(x-7) = (x^2+49)/(x^2-49)

Note that x^2-49 = (x-7)(x+7).

Multiply both sides by (x-7)(x+7).

x(x-7) - 7(x+7) = x^2 +49

x^2 -7x -7x -49 = x^2 +49

-14x - 49 = 49

-14x = 98

x = -7

Does this solution work in the original equation?

I'll let you determine that.

I'll also let you attempt the rest.