# Divide (2/(x+2)+10/(x+5))÷((7x+20)/(x^2+7x+10))

(2x+2+10x+5)÷7x+20×2+7x+10
To divide by a fraction, multiply by its reciprocal.
(2x+2+10x+5)x2+7x+107x+20
Factor x2+7x+10 using the AC method.
Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is 10 and whose sum is 7.
2,5
Write the factored form using these integers.
(2x+2+10x+5)(x+2)(x+5)7x+20
(2x+2+10x+5)(x+2)(x+5)7x+20
To write 2x+2 as a fraction with a common denominator, multiply by x+5x+5.
(2x+2⋅x+5x+5+10x+5)(x+2)(x+5)7x+20
To write 10x+5 as a fraction with a common denominator, multiply by x+2x+2.
(2x+2⋅x+5x+5+10x+5⋅x+2x+2)(x+2)(x+5)7x+20
Write each expression with a common denominator of (x+2)(x+5), by multiplying each by an appropriate factor of 1.
Multiply 2x+2 and x+5x+5.
(2(x+5)(x+2)(x+5)+10x+5⋅x+2x+2)(x+2)(x+5)7x+20
Multiply 10x+5 and x+2x+2.
(2(x+5)(x+2)(x+5)+10(x+2)(x+5)(x+2))(x+2)(x+5)7x+20
Reorder the factors of (x+5)(x+2).
(2(x+5)(x+2)(x+5)+10(x+2)(x+2)(x+5))(x+2)(x+5)7x+20
(2(x+5)(x+2)(x+5)+10(x+2)(x+2)(x+5))(x+2)(x+5)7x+20
Combine the numerators over the common denominator.
2(x+5)+10(x+2)(x+2)(x+5)⋅(x+2)(x+5)7x+20
Simplify the numerator.
Factor 2 out of 2(x+5)+10(x+2).
Factor 2 out of 10(x+2).
2(x+5)+2(5(x+2))(x+2)(x+5)⋅(x+2)(x+5)7x+20
Factor 2 out of 2(x+5)+2(5(x+2)).
2(x+5+5(x+2))(x+2)(x+5)⋅(x+2)(x+5)7x+20
2(x+5+5(x+2))(x+2)(x+5)⋅(x+2)(x+5)7x+20
Apply the distributive property.
2(x+5+5x+5⋅2)(x+2)(x+5)⋅(x+2)(x+5)7x+20
Multiply 5 by 2.
2(x+5+5x+10)(x+2)(x+5)⋅(x+2)(x+5)7x+20
2(6x+5+10)(x+2)(x+5)⋅(x+2)(x+5)7x+20
2(6x+15)(x+2)(x+5)⋅(x+2)(x+5)7x+20
Factor 3 out of 6x+15.
Factor 3 out of 6x.
2(3(2x)+15)(x+2)(x+5)⋅(x+2)(x+5)7x+20
Factor 3 out of 15.
2(3(2x)+3(5))(x+2)(x+5)⋅(x+2)(x+5)7x+20
Factor 3 out of 3(2x)+3(5).
2(3(2x+5))(x+2)(x+5)⋅(x+2)(x+5)7x+20
2⋅3(2x+5)(x+2)(x+5)⋅(x+2)(x+5)7x+20
Multiply 2 by 3.
6(2x+5)(x+2)(x+5)⋅(x+2)(x+5)7x+20
6(2x+5)(x+2)(x+5)⋅(x+2)(x+5)7x+20
Cancel the common factor of (x+2)(x+5).
Cancel the common factor.
6(2x+5)(x+2)(x+5)⋅(x+2)(x+5)7x+20
Rewrite the expression.
6(2x+5)17x+20
6(2x+5)17x+20
Combine 17x+20 and 6.
67x+20(2x+5)
Multiply 67x+20 and 2x+5.
6(2x+5)7x+20
Divide (2/(x+2)+10/(x+5))÷((7x+20)/(x^2+7x+10))