Question

Express: x-2 x2-5x 6 x 3 23 - 9x as a single fraction in the form: ax b cx² dx where a, b, c and d are integers to be found.

Answer 1

The student's task is to simplify several expressions into a single fraction in the form ax + b / (cx² + dx), using exponent rules and algebraic simplification.

To express the given expression as a single fraction, factorize the quadratic expression and simplify each term. The final expression is (x²-5x+6)/(3x²-32x+207)

Step-by-step explanation:

To express the given expression as a single fraction, we need to find the common denominator. The denominators in the expression are x, x², and 1. To simplify the process, let's first factorize the quadratic expression.

We have: (x-2)(x²-5x+6)/(x(3x-23)-9x)

Now, let's simplify each term:

(x-2)(x-3)/(x-9)(3x-23)

Expanding the expression:

x²-5x+6/(3x²-32x+207)

Therefore, the expression can be written as:

(x²-5x+6)/(3x²-32x+207)