I have a test coming up and these are some sample questions on the test.
If any one can give me step by step help on how to solve that would be wonderful.
I have not done this in about 4 years so the more thorough the explanation the better please. Thank you!
1) Divide 25b² - 36 / b²+4ab+4a² by 5b+6 / 2a+b
2) Divide x⁵ - 32 by x +2
3) Write 5 - 2i / 3+ 2i in form of a + bi where a and b are real numbers.
4) Solve for x, 3 / x² - 4 = 2 / x + 2 + 5 / x - 2
5) Find all the values of x, ( √2x + 2) - (√x + 2 ) = 1
6) Find all the values of x, log₄x = - 3/2
7) Factor completely , 3x⁴y³ - 15x³y³ - 18x²y³
8) Compute (a) cot 2π / 3 (b) cos 5π / 4 (b) tan 7π / 4 (d) cos 3π
9) Simplify (a / 2b) / (1 / b²) - (2b / a ) / (1 / 2a)
If any one can give me step by step help on how to solve that would be wonderful.
I have not done this in about 4 years so the more thorough the explanation the better please. Thank you!
1) Divide 25b² - 36 / b²+4ab+4a² by 5b+6 / 2a+b
2) Divide x⁵ - 32 by x +2
3) Write 5 - 2i / 3+ 2i in form of a + bi where a and b are real numbers.
4) Solve for x, 3 / x² - 4 = 2 / x + 2 + 5 / x - 2
5) Find all the values of x, ( √2x + 2) - (√x + 2 ) = 1
6) Find all the values of x, log₄x = - 3/2
7) Factor completely , 3x⁴y³ - 15x³y³ - 18x²y³
8) Compute (a) cot 2π / 3 (b) cos 5π / 4 (b) tan 7π / 4 (d) cos 3π
9) Simplify (a / 2b) / (1 / b²) - (2b / a ) / (1 / 2a)
-
1- when you have a/b divided by c/d
you can flip the second one
(a/b)(d/c) and perform multiplication
3) Write 5 - 2i / 3+ 2i
put () or you will amke mistake.
multiply it by the denominator's reciprocal
den. is (3+2i) its reciprocal is (3-2i) why
(a+b)(a-b)= a²-b²
[(5 - 2i) / (3+ 2i )] [ (3-2i) / (3-2i) ] =
(5-2i) (3-2i)
------------------
(3+2i) (3-2i)
=
distribute top and bottom
(15 -10i -6i +4i²)
---------------------
( 3² - 4i²)
since i² =-1
=
(15 - 16i -4)
------------------
(9 +4)
you can take it from here.
4- you need () to make reader understand what you mean.
5-
since before () is (-) sign you can remove the () and change inner sign when it is approriate.
√2x + 2 - √x + 2 = 1
simplify adding like terms
assuming only 2 is under the root
(√2)x + 4 - √x = 1
move numbers to one side
(√2)x - √x = 1-4 = -3
square both sides
((√2)x - √x )² = (-3)²
distribute
(2x² +x - (2√2)(√x)) =9
since you square them up, you must test your solutions.
move all terms w/out root to one side.
(2x² -9) = 2√(2x)
square both sides again the repeat the step above.
you can flip the second one
(a/b)(d/c) and perform multiplication
3) Write 5 - 2i / 3+ 2i
put () or you will amke mistake.
multiply it by the denominator's reciprocal
den. is (3+2i) its reciprocal is (3-2i) why
(a+b)(a-b)= a²-b²
[(5 - 2i) / (3+ 2i )] [ (3-2i) / (3-2i) ] =
(5-2i) (3-2i)
------------------
(3+2i) (3-2i)
=
distribute top and bottom
(15 -10i -6i +4i²)
---------------------
( 3² - 4i²)
since i² =-1
=
(15 - 16i -4)
------------------
(9 +4)
you can take it from here.
4- you need () to make reader understand what you mean.
5-
since before () is (-) sign you can remove the () and change inner sign when it is approriate.
√2x + 2 - √x + 2 = 1
simplify adding like terms
assuming only 2 is under the root
(√2)x + 4 - √x = 1
move numbers to one side
(√2)x - √x = 1-4 = -3
square both sides
((√2)x - √x )² = (-3)²
distribute
(2x² +x - (2√2)(√x)) =9
since you square them up, you must test your solutions.
move all terms w/out root to one side.
(2x² -9) = 2√(2x)
square both sides again the repeat the step above.