Partial Fractions

Partial Fractions:

To express a single rational function as a sum of two or more single rational functions which are called Partial Fractions. For example,

Partial Fraction Resolution:

Expressing a rational function as a sum of partial fractions is called Partial Fraction Resolution. It is an extremely valuable tool in the study of calculus.

Equation:

An open sentence formed by using the sign of equality ' = ' is called an equation.

The equations can be divided into the following two kinds:

Conditional Equation:

It is an equation in which two algebraic expressions are equal for particular value/s of the variable e.g.,

• 2x = 3 is a conditional equation and it is true only if x = 3/2.
• x² + x - 6 = 0 is a conditional equation and it is true for x = 2, -3 only.

Important Note:

For simplicity, a conditional equation is called an equation.

Identity:

It is an equation which holds good for all values of the variable e.g.,

• (a + b)x ≡ ax + bx is an identity and its two sides are equal for all values of x.
• (x + 3)(x + 4) ≡ x² + 7x + 12 is also an identity which is true for all values of x.

For convenience, the symbol " = " shall be used both for equation and identity.