Simplify (x2 + 4x)/(2x + 8)

Algebra is the branch of mathematics in which we study numerals and variables.  Numerals are the number that has constant values and variables are the letters or symbols that do not have constant values. Algebra is basically used to find out the value of unknowns. We can formalize a common equation for all the same types of problems. 

For example:

 In a right-angled triangle, we have three sides. Suppose the base is represented by ‘B, perpendicular is represented by ‘P’, and the hypotenuse is represented by ‘H’ . Then according to Pythagoras theorem, 

H² = P² + B²

If two sides of a triangle are given then by putting the value in the above formula we can easily get the third side.

Algebraic Expression

The systematic arrangement of the numerals, variable, and arithmetic operators is known as an algebraic expression. For example, if we have to write the mathematical statement ‘three times a number subtracted from 16′ can be written as ’16 – 3x’. Here we suppose the unknowns as ‘x’ and form the mathematical expression according to the information given in the question.

In 16 – 3x, the Negative sign separates the expression into two terms. So on the basis of the number of terms the expression is classified into the following types.

• Monomial: If the number of terms in an expression is one then it is known as a monomial. Example: 6c, -9d, etc
• Binomial: If the number of terms in an expression is two then the expression is known as binomial. Example: 9x-3y, 9t+3u, etc.
• Trinomial: If the number of terms in an expression is three then the expression is known as trinomial. Example: a-c+d, 8e+3d-12c, etc.
• Polynomial: If the number of terms in an expression is one or more than one then the expression is known as a polynomial.

Factorization: When an expression is written in the multiplication form of two or more factors is called factorization. For example, 3x² can be written as 3×x×x. Here, 3, x is the factor of 3x².

Simplify (x² + 4x)/(2x + 8)

Solution: 

Step 1: Factorize the numerator and denominator.

= (x² + 4x)/(2x + 8)

In the numerator, x is present in both the terms so it can be common. Similarly in the denominator, 2 is present in both terms. 

= (x×x + 2×2×x)/(2×x + 2×2×2)

Take x common from numerator and 2 from denominator.

= {x(x+4)}/{2(x+4)}

Step 2: Cancel the common term of numerator and denominator.

(x+4) is present in the numerator and denominator, so it can be canceled out. Write the remaining term.

 = x/2

So the simplified form of the expression (x² + 4x)/(2x + 8) is x/2.

Similar Questions

Question 1: Factor the numerator and denominator of the fraction, if necessary. That is, rewrite as a product. Then look for ones and simplify. Assume the denominator is not zero. (a² + 12a)/(4a + 48)

Solution: 

Factorize the numerator and denominator.

= (a×a + 2×2×3×a)/(2×2×a + 2×2×2×2×3)

Take out the common factor from the numerator and denominator. 

= {a(a + 2×2×3)}/{2×2(a + 2×2×3)}

= {a(a + 12)}/{4(a + 12)}

Cancel the common term from the numerator and denominator.

= a/4

So the simplified form of the expression (a² + 12a)/(4a + 48) is a/4.

Question 2:  Factor the numerator and denominator of the fraction, if necessary. That is, rewrite as a product. Then look for ones and simplify. Assume the denominator is not zero. (p³ –  6p)/(3p² -18).

Solution:

Factorize the numerator and denominator.

= (p×p×p – 2×3×p)/(3×p×p – 2×3×3)

Take out the common factor from the numerator and denominator. 

= {p( p×p – 2×3)}/{3(p×p – 2×3)}

= {p(p²-6)}/{3(p² – 6)}

Cancel the common term from the numerator and denominator.

= p/3

So the simplified form of the expression(p³ –  6p)/(3p² -18) is p/3.