Question

please help me with the question in the picture

Answer 1

Answer:

(x - 5) / (x - 6) (don't put them in brackets, i'm doing this to signify that all of x - 5 is being divided by all of x - 6).

Step-by-step explanation:

x² + 2x - 35:

what multiplies into -35 and adds into 2?

7 and -5

so the top is now (x + 7)(x - 5)

x² + x - 42

what multiplies into -42 and adds into 1?

-6 and 7

so the bottom is now (x + 7)(x - 6)

the 2 lots of (x + 7) cancel and you are left with (x - 5) / (x - 6)

Answer 2

Answer:

$\frac{x-5}{x-6}$

Step-by-step explanation:

Let's start with the numerator to factor it.

We need two numbers adding up to 2 and multiplying to -35. Easy to see the number are +7 and -5. You can then factor as $x^2+2x-35=(x+7)(x-5)$

Denominator then. Same story, Two number adding to 1 and multiplying to -42. Numbers are +7 again and -6. Factors as before:

$x^2+x-42=(x+7)(x-6)$.

Now you can simplify

$\frac{x^2+2x-35}{x^2+x-42} = \frac{(x+7)(x-5)}{(x+7)(x-6)}= \frac{x-5}{x-6}$