The first step for solving this equation is to determine the defined range.
, x ≠ 1
Remember that when the denominators of both fractions are the same,, you need to set the numerators equal. This will look like the following:
= 5
Take the root of both sides of the equation and remember to use both positive and negative roots.
x +/-
![\sqrt[4]{5}](https://tex.z-dn.net/?f=%20%5Csqrt%5B4%5D%7B5%7D)
Separate the solutions.
x =
, x ≠ 1
x = -
Check if the solution is in the defined range.
x =
x = -
This means that the final solution to your question are the following:
x =
x = -
Let me know if you have any further questions.
:)
Answer:
fraction which has a terminating decimal as its decimal expansion is:
1/5
Step-by-step explanation:
We are given 4 fractions:
1/3 , 1/5 , 1/7 and 1/9
We have to find which fraction has terminating decimal.
1/3 = 0.33333...
1/5 = 0.2
1/7 = 0.142857142857...
1/9 =0.11111.....
Hence, fraction which has a terminating decimal as its decimal expansion is:
1/5
Answer:
2(n - 6) >= 22
Step-by-step explanation:
2n - 12 >= 22
2n >= 22+12
2n >= 34
n >= 34/2
n >= 17
Answer:
3:1
54:18
Step-by-step explanation:
You can divide both sides by 9 to get one ratio:
27/9:9/9
3:1
You can also multiply both sides by 2 to get another ratio:
27(2):9(2)
54:18
Answer:
1. (x - 3)² = 8
2. (x + 2)² = 3
3. (x + 6)² = 
4. (x + 3)² = 27
5. (x + 4)² = 13
6. 
Step-by-step explanation:
Completion of Square: 
In the following problems the terms in the RHS of the above equation may be missing. We balance the equation. Simplify it and re write it in terms of LHS.
1. x² - 6x + 1 = 0
Taking the constant term to the other side, we get:
x² - 6x = - 1
⇒ x² - 2(3)x = -1
⇒ x² -2(3)x + 9 = - 1 + 9 [Adding 9 to both the sides]
⇒ x² -2(3)x + 3² = 8
⇒ (x - 3)² = 8 is the answer.
2. 3x² + 12x + 3 = 0
Note that the co-effecient of x² is not 1. We make it 1, by dividing the whole equation by 3. And then proceed like the previous problem.
3x² + 12x = -3
Dividing by 3 through out, x² + 4x = - 1
⇒ x² + 2(2) + 4 = -1 + 4
⇒ x² +2(2) + 2² = 3
⇒ (x + 2)² = 3 is the answer.
3. 2x² + 24x = 29
x² + 12x = 
⇒ x² + 2(6)x + 36 = + 36
⇒ x² + 2(6)x + 6² = 
⇒ (x + 6)² = is the answer.
4. x² + 6x - 18 = 0
x² + 6x = 18
⇒ x² + 2(3)x = 18
⇒ x² + 2(3)x + 9 = 18 + 9
⇒ x² + 2(3)x + 3² = 27
⇒ (x + 3)² = 27 is the answer.
5. x² + 8x + 3 = 0
x² + 8x = -3
⇒ x² + 2(4)x = -3
⇒ x² + 2(4)x + 16 = - 3 + 16
⇒ x² + 2(4)x + 16 = 13
⇒ (x + 4)² = 13 is the answer.
6. 9x² - 30x + 6 = 0
9x² - 30x = - 6
⇒ x² 
x = - 6
is the answer.
