Express in simplest form: (2x^(2)-8x-42)/(6x^(2))÷(x^(2)-9)/(x^(2)-3x)

Question

Express in simplest form:  (2x^(2)-8x-42)/(6x^(2))÷(x^(2)-9)/(x^(2)-3x)

Bytelearn · Accepted Answer

Multiply by Reciprocal: Simplify the division of fractions by multiplying by the reciprocal. To divide by a fraction, you multiply by its reciprocal. The reciprocal of (x^(2)-9)/(x^(2)-3x) is (x^(2)-3x)/(x^(2)-9).Set up Multiplication: Set up the multiplication of the two fractions. (2x^(2)-8x-42)/(6x^(2)) * (x^(2)-3x)/(x^(2)-9)Factor Numerators and Denominators: Factor the numerators and denominators where possible. The numerator 2x^(2)-8x-42 can be factored as 2(x^(2)-4x-21). The denominator x^(2)-9 can be factored as (x+3)(x-3). The denominator x^(2)-3x can be factored as x(x-3). So the expression becomes: 2(x^(2)-4x-21)/(6x^(2)) * x(x-3)/((x+3)(x-3))Simplify by Canceling Common Factors: Simplify the expression by canceling out common factors. The x-3 in the numerator and denominator cancels out, as does one x from x(x-3) and one x from 6x^(2), leaving a 6 in the denominator. The expression now looks like this: 2(x^(2)-4x-21)/(6x) * x/(x+3)Further Simplify Expression: Further simplify the expression. The 2 in the numerator and the 6 in the denominator can be simplified to 1/3. The expression now looks like this: (1/3)(x^(2)-4x-21)/x * x/(x+3)Cancel Common X Factor: Cancel out the common x factor in the numerator and denominator. The x in the numerator and the x in the denominator cancel out. The expression now looks like this: (1/3)(x^(2)-4x-21)/(x+3)Distribute 1/3 Across Numerator: Distribute the 1/3 across the numerator. (1/3)x^(2) - (4/3)x - 7/(x+3)Check for Further Simplification: Check if the expression can be simplified further. The expression (1/3)x^(2) - (4/3)x - 7/(x+3) is already in its simplest form. There are no common factors that can be canceled out.

Express in simplest form: $\frac{2 x^{2}-8 x-42}{6 x^{2}} \div \frac{x^{2}-9}{x^{2}-3 x}$

Full solution

More problems from Divide polynomials using long division

Related topics

Express in simplest form: 2x2−8x−426x2÷x2−9x2−3x \frac{2 x^{2}-8 x-42}{6 x^{2}} \div \frac{x^{2}-9}{x^{2}-3 x} 6x22x2−8x−42​÷x2−3xx2−9​

Express in simplest form: $\frac{2 x^{2}-8 x-42}{6 x^{2}} \div \frac{x^{2}-9}{x^{2}-3 x}$