Simplify:
-12x^4
x^4+8x^5
A -12 ; x ≠-1/8
1+8x
B -12 ; x ≠ -1/8, 0
1+8x
C -12 ; x ≠ 0
9x
D -12
9
Simplify:
x
7x+x^2
A 1 ; x ≠ -7
7+x
B 1 ; x ≠ 0
7x
C 1 ; x ≠ 0,-7
7+x
D 1
7
Simplify:
x-2
x^2+4x-12
A 1 ; x ≠ -6
x+6
B 1 ; x ≠ -6,
x+6
C 1 ; x ≠ -2
x+2
D x+2
Simplify:
x^2-3x-18
x+3
A x-3
B x-6 ; x ≠ -3
C x-6 ; x ≠ 6
D 1 ; x ≠ -3
x+3
For example, the first one:
-12x^4 / (x^4+8x^5)
= -12x^4 / (x^4(1+8x))
division by zero is undefined, so B is the right choice
why not A? Because the original fraction is 0/0 if x=0
You need to type your fractions as I did, rather than trying to copy/paste into plain text.
If you factor each of them and then set your answer = 0 you will be able to pick out a multiple choice answer that fits each scenerio.
You try them...
Submit your answers...
and we will check them : )
For example x^2 - 3x - 18 = (x -6)(x+3)
To simplify the expressions, follow these steps:
1. For the first expression, -12x^4, there is no simplification possible. So the answer is -12x^4.
2. For the second expression, x^4+8x^5, you can factor out x^4 to get x^4(1+8x). So the answer is -12x^4, x^4(1+8x).
Now let's simplify the next set of expressions:
1. For the expression x/(7x+x^2), you can factor out x to get x/(x(7+x)). Cancel out one of the x terms to get 1/(7+x). So the answer is 1/(7+x).
2. For the expression (x-2)/(x^2+4x-12), you can factor the denominator to get (x-2)/((x+6)(x-2)). Cancel out the (x-2) terms to get 1/(x+6). So the answer is 1/(x+6).
Therefore, the answers are:
-12x^4, x^4(1+8x), 1/(7+x), and 1/(x+6).
To simplify expressions, we need to perform the operations indicated. Let's go through each question and find the correct answer.
1) Simplify: -12x^4 / (x^4+8x^5)
To simplify this expression, we can first factor out a common term of x^4 from both the numerator and denominator:
-12x^4 / (x^4(1+8x))
Now divide -12x^4 by x^4:
-12 / (1+8x)
The simplified expression is -12 / (1+8x). However, we need to consider any restrictions on the variables. In this case, x cannot be equal to -1/8, as it would result in division by zero. So the final answer is:
A -12 ; x ≠ -1/8, 0
1+8x
2) Simplify: x / (7x + x^2)
To simplify this expression, we first factor out a common term of x from the denominator:
x / (x(7 + x))
Now divide x by x:
1 / (7 + x)
The simplified expression is 1 / (7 + x). However, we need to consider any restrictions on the variables. In this case, x cannot be equal to 0 or -7, as it would result in division by zero. So the final answer is:
C 1 ; x ≠ 0,-7
7+x
3) Simplify: (x-2) / (x^2 + 4x - 12)
To simplify this expression, we need to factor the denominator:
(x-2) / ((x+6)(x-2))
Notice that the term (x-2) appears in both the numerator and denominator. We can cancel it out, resulting in:
1 / (x+6)
The simplified expression is 1 / (x+6). However, we need to consider any restrictions on the variables. In this case, x cannot be equal to -6, as it would result in division by zero. So the final answer is:
B 1 ; x ≠ -6
x+6
4) Simplify: (x^2-3x-18) / (x+3)
To simplify this expression, we can divide the numerator by the denominator using polynomial long division or synthetic division:
x - 6
----------------
x + 3 | x^2 - 3x - 18
- (x^2 + 3x)
--------------
-6x - 18
+ (6x + 18)
---------------
0
So the result of the division is x - 6.
The simplified expression is x - 6. However, we need to consider any restrictions on the variables. In this case, x cannot be equal to -3, as it would result in division by zero. So the final answer is:
B x-6 ; x ≠ -3