Question

Show that (1)/(2x²+x-15)/(1)/(3x²+9x) simplies to (ax)/(bx+c), where a,b and c are integers to be found.

Answer 1

To show that (1)/(2x²+x-15)/(1)/(3x²+9x) simplifies to (ax)/(bx+c), we need to perform the division and simplify the resulting expression. We can simplify the expression by factoring the numerator and denominator and canceling out any common factors. The simplified expression is (3x)/(2x-5) where a = 3, b = 2, and c = -5.

Step-by-step explanation:

To show that (1)/(2x²+x-15)/(1)/(3x²+9x) simplifies to (ax)/(bx+c), we need to perform the division and simplify the resulting expression.

1. First, flip the second fraction to get (1)/(2x²+x-15) * (3x²+9x)/(1).
2. Next, multiply the numerators and denominators: (1 * 3x²+9x)/(2x²+x-15 * 1).
3. Simplify the expression to get (3x²+9x)/(2x²+x-15).

To further simplify the expression and make it in the form (ax)/(bx+c), we can factor the numerator and denominator and cancel out any common factors. By factoring the numerator and denominator, we get 3x(x+3) and (2x-5)(x+3).

Therefore, the simplified expression is (3x(x+3))/((2x-5)(x+3)), which can be written as (3x)/(2x-5) where a = 3, b = 2, and c = -5.