Question

Answer these questions about the steps of simplifying this rational expression:

Part A What is the GCF of the terms in the numerator and denominator? Rewrite the expression by factoring out any common factors.

Part B Write the quadratic expressions in the numerator and the denominator in factored form.

Part C Cancel the common factor of the numerator and the denominator to write the expression in simplified form.

Answer 1

x²

Explanation:

4x²-14x+6

x²-7x²+12x

=2×2×x×x-2×7×x+2×3

x×x×x-7×x×x+2×2×3

= -2+2

x×x

the 2s cancle each other

= x²

Answer 2

The GCF values of the numerator and denominator are : 2 and x respectively.

The quadratic form of the expression is : (x - 3)(x - 1/2) / (x² - 4x)(x - 3)

The simplified form of the expression is : (x - 1/2) / (x² - 4x)

Using the expression given :

• 4x² - 14x + 6 / x³ - 7x² + 12x

Part A.

The GCF of the numerator , 4x² , -14x and 6 is 2

The GCF of the denominator , x³ , -7x² and 12x is x ;

Part B:

Numerator:

2x² - 7x + 3

x² -7x/2 + 3/2

x(x - 3) -1/2(x - 3)

(x - 3)(x - 1/2)

Denominator:

x³ - 7x² + 12x

x²(x-3) -4x(x-3)

(x²-4x)(x-3)

Expressing in quotient form:

(x - 3)(x - 1/2) / (x² - 4x)(x - 3)

Part C:

(x - 3)(x - 1/2) / (x² - 4x)(x - 3) = (x - 1/2) / (x² - 4x)

Hence, the simplified form of the expression is : (x - 1/2) / (x² - 4x)