Category: Algebra
"Published in Newark, California, USA"
Find the factors for
Solution:
The given equation above is a quadratic equation where the variables or terms are polynomials like (2x - 1) and (x + 3).
To test the above equation if it is factorable or not, let's consider the following procedure: if a = 8, b = -2, and c = -3, then using the discriminant formula, we have
Since the value of discriminant is a perfect square, then the given equation is factorable. Consider the given equation above
Factor the above equation in terms of (2x - 1) and (x + 3), we have

This website will show the principles of solving Math problems in Arithmetic, Algebra, Plane Geometry, Solid Geometry, Analytic Geometry, Trigonometry, Differential Calculus, Integral Calculus, Statistics, Differential Equations, Physics, Mechanics, Strength of Materials, and Chemical Engineering Math that we are using anywhere in everyday life. This website is also about the derivation of common formulas and equations. (Founded on September 28, 2012 in Newark, California, USA)
Tuesday, May 14, 2013
Monday, May 13, 2013
Special Products - Rational Functions
Category: Algebra
"Published in Newark, California, USA"
Write the product and simplify for
"Published in Newark, California, USA"
Write the product and simplify for

Solution:
The given equation above is another good example of special products where a binomial multiplied by another binomial where the terms are rational functions. In this case, we have to do the distribution property of multiplication over addition as follows
The LCD (Least Common Denominator) of the three fractions is (x + y)2(a + b)2. Rewrite the three fractions in terms of their LCD and simplify, we have
Since all the terms of the numerator cannot be combined and simplified, then we can leave the final answer as is.
Sunday, May 12, 2013
Inverse Trigonometric Functions
Category: Trigonometry, Algebra
"Published in Suisun City, California, USA"
Rewrite the expression as an algebraic expression in x for
Solution:
Consider the given equation above, we have
Let
and
so that the above equation becomes
Next, we need to get the values of trigonometric functions as a function of x. Consider again the given inverse trigonometric functions in order to get the trigonometric functions as a function of x as follows:
Let
Draw and label a right triangle in order to get the other trigonometric functions as a function of x
Let
Draw and label a right triangle in order to get the other trigonometric functions as a function of x
Finally, consider again the function
Substitute the values of trigonometric functions to the above equation, we have
Rationalize the denominator in order to eliminate the radical sign
Therefore,
"Published in Suisun City, California, USA"
Rewrite the expression as an algebraic expression in x for
Solution:
Consider the given equation above, we have
Let
and
so that the above equation becomes
Next, we need to get the values of trigonometric functions as a function of x. Consider again the given inverse trigonometric functions in order to get the trigonometric functions as a function of x as follows:
Let
Draw and label a right triangle in order to get the other trigonometric functions as a function of x
![]() |
Photo by Math Principles in Everyday Life |
Let
Draw and label a right triangle in order to get the other trigonometric functions as a function of x
![]() |
Photo by Math Principles in Everyday Life |
Finally, consider again the function
Substitute the values of trigonometric functions to the above equation, we have
Rationalize the denominator in order to eliminate the radical sign
Therefore,
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