A Complete Guide To Solve Undefined Fractions

A fraction is said to be undefined if the denominator is zero, e.g 9/0, 2/0, 3/0 etc.

For instance, 1/x+2 is undefined

If the value of x = -2

When x = -2,

Then 1/x+2 = 1/-2+2 = 1/0

Division by zero is in possible therefore, the fraction 1/x+2 is said to be undefined when x=-2

Given a fraction Nx/Dx where Nx is the numerator and Dx the denominator, the fraction Nx/Dx will be said to be undefined if the denominator Dx is equal to zero.

Now that we are conversant with the procedure to be used when dealing with undefined fraction, let solve some important problems.

Example 1:

Find the values of x for which the fraction x+2/x²-3x-10 is undefined

Solution

Recall that a fraction is said to be undefined if the denominator is equal to zero

That means

x²-3x=10 – 0

Since it is a quadratic equation, we need to solve by factorization

x²-3x=10 – 0

The last and first terms are -10 and x²

-10 x x² = -10x²

The middle term is -3x

Two factorization in x whose sum will give -3x and product will give -10x² are -5x and 2x

We replace -3x with -5x and 2x

x2 + 2x-5x-10 = 0

x(x+2)-5(x+2) = 0

(x+2) (x-5) = 0

x + 2 = 0 and x – 5 = 0

x =2 or x =5

The fraction is undefined which x = -2 or x = 5

Example 2

What are the values of x for which the expression

6x + 1/x²-18x-20 is not defined?

Solution

X will be undefined when x2+8x-20 = 0

We solve again by factorization

The first term is x² and the last term is -20

The product is x²– 20 = -20x²

The middle term = +8x

The two factors in 8 whose sum gives +8x and product gives -20x² are 10x and -2x

(x²+10x)-(2x-20) = 0

x(x +10)-2 (x+10) = 0

(x+10) (x+2) = 0

x + 10 = 0 and x -2 =0

x = -10 or x =2

Therefore, the expression is undefined if x = 10 or x =2

Read Also:

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• See How to Construct Quadratic Equation
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• How to Solve Quadratic Equation by Factorization

Example 3:

• For what values of x is the expression

2x-16/x²-11x+24

• For what value of x is the expression equal to zero

Solution

• The expression is undefined when its denominator

x²=11x+24 is zero

i.ex²-11x+24 = 0

The first term is x²and the last term is 24

The product yield x²x24 = 24x²

The middle term is -11x

Two factors in x whose sum gives -11x and product gives 24x² are -8x and -3x

We the replace -11x with the factors

x²-8x-3x+24=0

x(x-8)-3(x-8) =0

(x-8) (x-3) = 0

x-8 = 0 or x – 3 =0

therefore, the expression is undefined of x = 8 or x = 0

• The expression is zero which the algebraic expression is equal to zero i.e

2x+16=0

2x/2 = 16/8

x = 8

the expression will be zero when x = 8

Example 4:

Find the value of x for which the algebraic fraction is undefined

9/x + x²-1/x²-16

Solution

Multiply both sides of the expression by the L.C.M  x(x²-16)

x(x²-16) x 9/x + x(x²-16) x²-1/x²-10

9(x²-16) +x(x²-1)

But the expression will be undefined when

x²=16 = 0

x²=16

Take square root of both sides

x^2x1/2 =

x = ± 4

which means x = -4 or x = 4 therefore the expression is undefined when x = 4 or -4 or 0

Example 5:

• For what values of x is the expression

2(x-1) /x²– 9 undefined

• For what values of A is the expression zero?

Solution

• The expression is undefined when its denominator

x² – 9 is zero

i.ex² – 9 = 0

x =9

take the square roots of both sides

x^2x½ =

x = ± 3

That means x = 3 or -3, therefore the fraction is undefined when x = -3 or 2

• The expression is zero when the algebraic expression, (the numerator) is equal to zero

i.e3(x-1) = 0

3x – 3 = 0

3x/3 = 3/3

x = 1

the expression will be zero when x = 1

If you have any questions about undefined fraction, kindly let us know in the comment box.