Trigonometry Examples

Solve for x -41/(5x^2)*1+2/(5x)-2 4/5=0
Step 1
Simplify the left side.
Tap for more steps...
Step 1.1
Simplify .
Tap for more steps...
Step 1.1.1
Convert to an improper fraction.
Tap for more steps...
Step 1.1.1.1
A mixed number is an addition of its whole and fractional parts.
Step 1.1.1.2
Add and .
Tap for more steps...
Step 1.1.1.2.1
To write as a fraction with a common denominator, multiply by .
Step 1.1.1.2.2
Combine and .
Step 1.1.1.2.3
Combine the numerators over the common denominator.
Step 1.1.1.2.4
Simplify the numerator.
Tap for more steps...
Step 1.1.1.2.4.1
Multiply by .
Step 1.1.1.2.4.2
Add and .
Step 1.1.2
Multiply by .
Step 2
Find the LCD of the terms in the equation.
Tap for more steps...
Step 2.1
Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
Step 2.2
Since contains both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part then find LCM for the variable part .
Step 2.3
The LCM is the smallest positive number that all of the numbers divide into evenly.
1. List the prime factors of each number.
2. Multiply each factor the greatest number of times it occurs in either number.
Step 2.4
Since has no factors besides and .
is a prime number
Step 2.5
The number is not a prime number because it only has one positive factor, which is itself.
Not prime
Step 2.6
The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either number.
Step 2.7
The factors for are , which is multiplied by each other times.
occurs times.
Step 2.8
The factor for is itself.
occurs time.
Step 2.9
The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either term.
Step 2.10
Multiply by .
Step 2.11
The LCM for is the numeric part multiplied by the variable part.
Step 3
Multiply each term in by to eliminate the fractions.
Tap for more steps...
Step 3.1
Multiply each term in by .
Step 3.2
Simplify the left side.
Tap for more steps...
Step 3.2.1
Simplify each term.
Tap for more steps...
Step 3.2.1.1
Cancel the common factor of .
Tap for more steps...
Step 3.2.1.1.1
Move the leading negative in into the numerator.
Step 3.2.1.1.2
Cancel the common factor.
Step 3.2.1.1.3
Rewrite the expression.
Step 3.2.1.2
Rewrite using the commutative property of multiplication.
Step 3.2.1.3
Cancel the common factor of .
Tap for more steps...
Step 3.2.1.3.1
Factor out of .
Step 3.2.1.3.2
Cancel the common factor.
Step 3.2.1.3.3
Rewrite the expression.
Step 3.2.1.4
Cancel the common factor of .
Tap for more steps...
Step 3.2.1.4.1
Factor out of .
Step 3.2.1.4.2
Cancel the common factor.
Step 3.2.1.4.3
Rewrite the expression.
Step 3.2.1.5
Cancel the common factor of .
Tap for more steps...
Step 3.2.1.5.1
Move the leading negative in into the numerator.
Step 3.2.1.5.2
Factor out of .
Step 3.2.1.5.3
Cancel the common factor.
Step 3.2.1.5.4
Rewrite the expression.
Step 3.3
Simplify the right side.
Tap for more steps...
Step 3.3.1
Multiply .
Tap for more steps...
Step 3.3.1.1
Multiply by .
Step 3.3.1.2
Multiply by .
Step 4
Solve the equation.
Tap for more steps...
Step 4.1
Use the quadratic formula to find the solutions.
Step 4.2
Substitute the values , , and into the quadratic formula and solve for .
Step 4.3
Simplify.
Tap for more steps...
Step 4.3.1
Simplify the numerator.
Tap for more steps...
Step 4.3.1.1
Raise to the power of .
Step 4.3.1.2
Multiply .
Tap for more steps...
Step 4.3.1.2.1
Multiply by .
Step 4.3.1.2.2
Multiply by .
Step 4.3.1.3
Subtract from .
Step 4.3.1.4
Rewrite as .
Step 4.3.1.5
Rewrite as .
Step 4.3.1.6
Rewrite as .
Step 4.3.1.7
Rewrite as .
Tap for more steps...
Step 4.3.1.7.1
Factor out of .
Step 4.3.1.7.2
Rewrite as .
Step 4.3.1.8
Pull terms out from under the radical.
Step 4.3.1.9
Move to the left of .
Step 4.3.2
Multiply by .
Step 4.3.3
Simplify .
Step 4.4
The final answer is the combination of both solutions.