Simplifying Complex Fraction, 2

Category: Algebra

"Published in Newark, California, USA"

Simplify

Solution:

Consider the give equation above

Get the Least Common Denominator (LCD) at the numerator and denominator and then simplify, we have

Get the reciprocal of the divisor and perform the multiplication, we have

Simplify the above equation and therefore,

Integration - Algebraic Substitution

Category: Integral Calculus, Algebra

"Published in Suisun City, California, USA"

Evaluate

Solution:

Consider the given equation above

Since there's a radical function in the denominator that is included in the polynomial, we have to eliminate the radical function by algebraic substitution as follows

Let 

Substitute the above values to the given equation, we have

But

Therefore,

Variable Separation, 2

Category: Differential Equations, Integral Calculus

"Published in Newark, California, USA"

Find the general solution for

Solution:

Consider the given equation above

Divide both sides of the equation by tan x tan y, we have

Integrate both sides of the equation

Apply the laws of logarithm for the above equation, we have

Take the inverse natural logarithm on both sides of the equation

Therefore,