Answer:
[tex] \dfrac{x + 7}{3} [/tex]
Step-by-step explanation:
Note: There may be a typo mistake in the question. It must be:
[tex] \dfrac{x^2 + 12x + 35}{3x + 15} [/tex]
To simplify the given expression [tex]\dfrac{x^2 + 12x + 35}{3x + 15}[/tex], we can factor the numerator and denominator and cancel common factors:
[tex] \dfrac{x^2 + 12x + 35}{3x + 15} [/tex]
Factor the numerator:
[tex] \dfrac{x^2 + (5+7)x + 35}{3x + 15} [/tex]
[tex] \dfrac{x^2 + 5x +7x + 35}{3x + 15} [/tex]
[tex] \dfrac{x(x+5)+7(x+5)}{3x + 15} [/tex]
[tex] \dfrac{(x + 5)(x + 7)}{3x + 15} [/tex]
Factor out the common factor in the denominator:
[tex] \dfrac{(x + 5)(x + 7)}{3(x + 5)} [/tex]
Now, cancel the common factor of [tex]x + 5[/tex] in the numerator and denominator:
[tex] \dfrac{\cancel{(x + 5)}(x + 7)}{3\cancel{(x + 5)}} [/tex]
The simplified expression is:
[tex] \dfrac{x + 7}{3} [/tex]
