To simplify this expression, we need to first factor the numerator and denominator:
Factor the numerator:x^2 - 10x + 25= (x - 5)(x - 5)= (x - 5)^2
Factor the denominator:3x + 12= 3(x + 4)
2x - 10= 2(x - 5)
x^2 - 16= (x + 4)(x - 4)
Now, our expression becomes:
((x - 5)^2) / (3(x + 4)(x - 5)) ÷ (2(x - 5) / (x + 4)(x - 4))
Next, we rewrite the expression by multiplying by the reciprocal of the second fraction:
((x - 5)^2) / (3(x + 4)(x - 5)) * ((x + 4)(x - 4) / 2(x - 5))
Now, we cancel out common factors:
(x - 5) / 3 (x + 4) (x - 4) / 2
Which simplifies to:
(x - 5)(x + 4)(x - 4) / 6
So, the simplified expression is:
To simplify this expression, we need to first factor the numerator and denominator:
Factor the numerator:
x^2 - 10x + 25
= (x - 5)(x - 5)
= (x - 5)^2
Factor the denominator:
3x + 12
= 3(x + 4)
2x - 10
= 2(x - 5)
x^2 - 16
= (x + 4)(x - 4)
Now, our expression becomes:
((x - 5)^2) / (3(x + 4)(x - 5)) ÷ (2(x - 5) / (x + 4)(x - 4))
Next, we rewrite the expression by multiplying by the reciprocal of the second fraction:
((x - 5)^2) / (3(x + 4)(x - 5)) * ((x + 4)(x - 4) / 2(x - 5))
Now, we cancel out common factors:
(x - 5) / 3 (x + 4) (x - 4) / 2
Which simplifies to:
(x - 5)(x + 4)(x - 4) / 6
So, the simplified expression is:
(x - 5)(x + 4)(x - 4) / 6