№3 ((y+5)/(y^2-7y+10)-(y-2)/(y^2-3y-10))/((11y+6)/(y^2-4))

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вопрос

To simplify the given expression:

Factor the denominators in both terms of the numerator and in the denominator:

Therefore, the numerator becomes ((y+5)/((y-2)(y-5)) - (y-2)/((y-5)(y+2)))

Combine the two terms in the numerator using a common denominator:
((y+5)(y+2) - (y-2)(y-5))/((y-2)(y-5)(y+2))

This simplifies to ((y^2 + 7y + 10) - (y^2 - 7y + 10))/((y-2)(y-5)(y+2))
= (2*7y)/((y-2)(y-5)(y+2))
= (14y)/((y-2)(y-5)(y+2))

Get the final result by dividing the numerator by the denominator:
(14y)/((y-2)(y-5)(y+2)) ÷ ((11y+6)/((y-2)(y+2)))

Multiplying by the reciprocal of the denominator gives:
(14y)/((y-2)(y-5)(y+2)) * (((y-2)(y+2))/(11y+6))
= 14y(y-2)(y+2)/((y-2)(y-5)(y+2)(11y+6))
= 14y/((y-5)(11y+6))

Therefore, the simplified expression is 14y/((y-5)(11y+6))