Question 345422: 7/v+1 + 9/7v
Answer by haileytucki(390)   (Show Source):
You can put this solution on YOUR website! (7)/(v)+1+(9)/(7)*v=0 Any \ symbols are the +- sign and the ~ symbol is the square root of sign.
Multiply (9)/(7) by v to get (9v)/(7).
(7)/(v)+1+(9v)/(7)=0
Find the LCD (least common denominator) of (9v)/(7)+(7)/(v)+1+0.
Least common denominator: 7v
Multiply each term in the equation by 7v in order to remove all the denominators from the equation.
(9v)/(7)*7v+(7)/(v)*7v+1*7v=0*7v
Simplify the left-hand side of the equation by canceling the common factors.
9v^(2)+7v+49=0*7v
Multiply 0 by 7v to get 0.
9v^(2)+7v+49=0
Use the quadratic formula to find the solutions. In this case, the values are a=9, b=7, and c=49.
v=(-b\~(b^(2)-4ac))/(2a) where av^(2)+bv+c=0
Use the standard form of the equation to find a, b, and c for this quadratic.
a=9, b=7, and c=49
Substitute in the values of a=9, b=7, and c=49.
v=(-7\~((7)^(2)-4(9)(49)))/(2(9))
Simplify the section inside the radical.
v=(-7\7i~(35))/(2(9))
Simplify the denominator of the quadratic formula.
v=(-7\7i~(35))/(18)
First, solve the + portion of \.
v=(-7+7i~(35))/(18)
Simplify the expression to solve for the + portion of the \.
v=(7(-1+i~(35)))/(18)
Next, solve the - portion of \.
v=(-7-7i~(35))/(18)
Simplify the expression to solve for the - portion of the \.
v=(7(-1-i~(35)))/(18)
The final answer is the combination of both solutions.
v=(7(-1+i~(35)))/(18),(7(-1-i~(35)))/(18)
If you want to simplify this and not solve the answer is:
(7)/(v)+1+(9)/(7)*v
Multiply (9)/(7) by v to get (9v)/(7).
(7)/(v)+1+(9v)/(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 7v. Next, multiply each fraction by a factor of 1 that will create the LCD in each of the fractions.
(9v)/(7)*(v)/(v)+(7)/(v)*(7)/(7)+1*(7v)/(7v)
Complete the multiplication to produce a denominator of 7v in each expression.
(9v^(2))/(7v)+(49)/(7v)+(7v)/(7v)
Combine the numerators of all expressions that have common denominators.
(9v^(2)+49+7v)/(7v)
Reorder the polynomial 9v^(2)+49+7v alphabetically from left to right, starting with the highest order term.
(9v^(2)+7v+49)/(7v)
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