Question

Simplify the following expression completely.

start fraction, x, squared, minus, 17, x, plus, 70, divided by, x, squared, minus, 18, x, plus, 80, end fraction
x
2
−18x+80
x
2
−17x+70
​

Answer 1

[AI-generated answer — Bot GPT 3.5]

To simplify the expression completely, we can factor the numerator and denominator.

Factoring the numerator:
x^2 - 17x + 70 = (x - 10)(x - 7)

Factoring the denominator:
x^2 - 18x + 80 = (x - 10)(x - 8)

Now we can cancel out the common factors:
(x - 10)(x - 7) / (x - 10)(x - 8)

Finally, we have:
(x - 7) / (x - 8)

Answer 2

[AI-generated answer — Step-by-Step Bot]

To simplify the expression completely, we can start by factorizing the numerator and the denominator.

The numerator can be factored as:
x^2 - 17x + 70 = (x - 10)(x - 7)

The denominator can be factored as:
x^2 - 18x + 80 = (x - 10)(x - 8)

Now, we can cancel out the common factors:
(x - 10)(x - 7) / (x - 10)(x - 8)

The common factor of (x - 10) in the numerator and denominator can be canceled out, leaving us with:
(x - 7) / (x - 8)

Therefore, the simplified expression is (x - 7) / (x - 8).

Answer 3

[AI-generated answer — Explain Bot]

To simplify the given expression completely, we can try to factor the numerator and the denominator individually and then cancel out any common factors.

Let's start with factoring the numerator: x^2 - 17x + 70.

To factor this quadratic expression, we need to find two numbers whose product is 70 and whose sum is -17 (since the coefficient of x^2 is 1). These numbers are -10 and -7.

So, we can rewrite the numerator as (x - 10)(x - 7).

Now let's factor the denominator: x^2 - 18x + 80.

Similarly, we need to find two numbers whose product is 80 and whose sum is -18. These numbers are -10 and -8.

So, we can rewrite the denominator as (x - 10)(x - 8).

Now, we can simplify the whole expression by canceling out the common factor of (x - 10) in the numerator and denominator:

start fraction, (x - 7), divided by, (x - 8), end fraction.

So, the simplified expression is (x - 7)/(x - 8).