Algebra with Fractions

Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures. Together with geometry, analysis, topology, combinatorics, and number theory, algebra is one of the main branches of pure mathematics.

Algebra with fraction example:
For what value of y is the following algebraic expression undefined.
y -  2
---------
y -  4

Solution:
The expression is approximate when y - 2 = 0.
Solve for y, we get y = 4
So the algebraic expression is undefined when y = 4.

algebra with fractions example 1:-

Problem 1: Simplify the following fraction equation

1      +      4
(x + 2)      (x + 3)

Solution:

Do the cross multiplication

=  1(x + 3) + 4(x + 2)
(x + 2)(x + 3)

=   x + 3 + 4x + 8
(x + 1)(x + 6)

Group the items

=     5x + 11
(x + 1)(x + 6)
Problem 2: Simplify the following fraction equation

10      -   2   = 1
(x + 4)       x

Multiply both sides by x(x + 4):

10x(x + 4) - 2x(x + 4) = x(x + 4)
(x + 4)            x

10x - 2(x + 4) = x2 + 4x

10x - 2x - 8 = x2 + 4x

Group the items

x2 - 4x + 8 = 0

Problem 3: Simplify the algebraic fraction
x3 − 3x + 1
-----------------
x2 + 2x − 3

Solution:

Factor the numerator and the denominator to obtain

x3 − 3x + 1 = (x − 1)3 , and x2 + 2x − 3 = (x − 1)(x + 3) .

Write the above equation as follows
(x − 1)2 × (x − 1)
=--------------------
(x + 3) × (x − 1)

Cancel the (x -1) to get
(x − 1)2
=-------------
(x + 3)

Problem 4:

28 is (2/7) of what number?

Solution:

Step 1: Assign variables:

Let x = number

Step 2: Solve the equation

28 = (2/7)x

x = 28(7/2)

Therefore x = 98

algebra with fractions Practice problem:-

x3 − 2x + 8
-----------------
x2 + 4x − 3