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Question 345343: (3/8-5/2i)-(5/6+1/7i)
Answer by haileytucki(390)   (Show Source):
You can put this solution on YOUR website! If you want it simplified the steps are:
((3)/(8)-(5)/(2)*i)-((5)/(6)+(1)/(7)*i)
Multiply -(5)/(2) by i to get -(5i)/(2).
((3)/(8)-(5i)/(2))-((5)/(6)+(1)/(7)*i)
Multiply (1)/(7) by i to get (i)/(7).
((3)/(8)-(5i)/(2))-((5)/(6)+(i)/(7))
Multiply -1 by each term inside the parentheses.
(3)/(8)-(5i)/(2)-(5)/(6)-(i)/(7)
To add fractions, the denominators must be equal. The denominators can be made equal by finding the least common denominator (LCD). In this case, the LCD is 24. Next, multiply each fraction by a factor of 1 that will create the LCD in each of the fractions.
-(5)/(6)*(4)/(4)+(3)/(8)*(3)/(3)-(5i)/(2)-(i)/(7)
Complete the multiplication to produce a denominator of 24 in each expression.
-(20)/(24)+(9)/(24)-(5i)/(2)-(i)/(7)
Combine the numerators of all fractions that have common denominators.
(-20+9)/(24)-(5i)/(2)-(i)/(7)
Add 9 to -20 to get -11.
(-11)/(24)-(5i)/(2)-(i)/(7)
Move the minus sign from the numerator to the front of the expression.
-(11)/(24)-(5i)/(2)-(i)/(7)
To add fractions, the denominators must be equal. The denominators can be made equal by finding the least common denominator (LCD). In this case, the LCD is 14. Next, multiply each fraction by a factor of 1 that will create the LCD in each of the fractions.
-(11)/(24)-(i)/(7)*(2)/(2)-(5i)/(2)*(7)/(7)
Complete the multiplication to produce a denominator of 14 in each expression.
-(11)/(24)-(2i)/(14)-(35i)/(14)
Combine the numerators of all expressions that have common denominators.
-(11)/(24)+(-2i-35i)/(14)
Combine all like terms in the numerator.
-(11)/(24)+(-37i)/(14)
Move the minus sign from the numerator to the front of the expression.
-(11)/(24)-(37i)/(14)
If you to to evaluate it:
((3)/(8)-(5)/(2)*i)-((5)/(6)+(1)/(7)*i)
Multiply -(5)/(2) by i to get -(5i)/(2).
((3)/(8)-(5i)/(2))-((5)/(6)+(1)/(7)*i)
Multiply (1)/(7) by i to get (i)/(7).
((3)/(8)-(5i)/(2))-((5)/(6)+(i)/(7))
Multiply -1 by each term inside the parentheses.
(3)/(8)-(5i)/(2)-(5)/(6)-(i)/(7)
To add fractions, the denominators must be equal. The denominators can be made equal by finding the least common denominator (LCD). In this case, the LCD is 24. Next, multiply each fraction by a factor of 1 that will create the LCD in each of the fractions.
-(5)/(6)*(4)/(4)+(3)/(8)*(3)/(3)-(5i)/(2)-(i)/(7)
Complete the multiplication to produce a denominator of 24 in each expression.
-(20)/(24)+(9)/(24)-(5i)/(2)-(i)/(7)
Combine the numerators of all fractions that have common denominators.
(-20+9)/(24)-(5i)/(2)-(i)/(7)
Add 9 to -20 to get -11.
(-11)/(24)-(5i)/(2)-(i)/(7)
Move the minus sign from the numerator to the front of the expression.
-(11)/(24)-(5i)/(2)-(i)/(7)
If you want it factored:
((3)/(8)-(5)/(2)*i)-((5)/(6)+(1)/(7)*i)
Multiply -(5)/(2) by i to get -(5i)/(2).
((3)/(8)-(5i)/(2))-((5)/(6)+(1)/(7)*i)
Multiply (1)/(7) by i to get (i)/(7).
((3)/(8)-(5i)/(2))-((5)/(6)+(i)/(7))
Multiply -1 by each term inside the parentheses.
(3)/(8)-(5i)/(2)-(5)/(6)-(i)/(7)
To add fractions, the denominators must be equal. The denominators can be made equal by finding the least common denominator (LCD). In this case, the LCD is 24. Next, multiply each fraction by a factor of 1 that will create the LCD in each of the fractions.
-(5)/(6)*(4)/(4)+(3)/(8)*(3)/(3)-(5i)/(2)-(i)/(7)
Complete the multiplication to produce a denominator of 24 in each expression.
-(20)/(24)+(9)/(24)-(5i)/(2)-(i)/(7)
Combine the numerators of all fractions that have common denominators.
(-20+9)/(24)-(5i)/(2)-(i)/(7)
Add 9 to -20 to get -11.
(-11)/(24)-(5i)/(2)-(i)/(7)
Move the minus sign from the numerator to the front of the expression.
-(11)/(24)-(5i)/(2)-(i)/(7)
To add fractions, the denominators must be equal. The denominators can be made equal by finding the least common denominator (LCD). In this case, the LCD is 14. Next, multiply each fraction by a factor of 1 that will create the LCD in each of the fractions.
-(11)/(24)-(i)/(7)*(2)/(2)-(5i)/(2)*(7)/(7)
Complete the multiplication to produce a denominator of 14 in each expression.
-(11)/(24)-(2i)/(14)-(35i)/(14)
Combine the numerators of all expressions that have common denominators.
-(11)/(24)+(-2i-35i)/(14)
Combine all like terms in the numerator.
-(11)/(24)+(-37i)/(14)
Move the minus sign from the numerator to the front of the expression.
-(11)/(24)-(37i)/(14)
Factor out the GCF of (1)/(2) from each term in the polynomial.
(1(-(11)/(12)))/(2)+(1(-(37i)/(7)))/(2)
Factor out the GCF of (1)/(2) from -(11)/(24)-(37i)/(14).
(1(-(11)/(12)-(37i)/(7)))/(2)
To add fractions, the denominators must be equal. The denominators can be made equal by finding the least common denominator (LCD). In this case, the LCD is 84. Next, multiply each fraction by a factor of 1 that will create the LCD in each of the fractions.
(1((-(11)/(12)*(7)/(7)-(37i)/(7)*(12)/(12))))/(2)
Complete the multiplication to produce a denominator of 84 in each expression.
(1((-(77)/(84)-(444i)/(84))))/(2)
Combine the numerators of all expressions that have common denominators.
(1(((-77-444i)/(84))))/(2)
Multiply 2 by 84 to get 168.
(-77-444i)/(168)
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