Divide (z/(z+2)+4/(5z))/(z/(7z+14)+9/z)

Math
zz+2+45zz7z+14+9z
Multiply the numerator and denominator of the complex fraction by (z+2)⋅5z(7z+14).
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Multiply zz+2+45zz7z+14+9z by (z+2)⋅5z(7z+14)(z+2)⋅5z(7z+14).
(z+2)⋅5z(7z+14)(z+2)⋅5z(7z+14)⋅zz+2+45zz7z+14+9z
Combine.
(z+2)⋅5z(7z+14)(zz+2+45z)(z+2)⋅5z(7z+14)(z7z+14+9z)
(z+2)⋅5z(7z+14)(zz+2+45z)(z+2)⋅5z(7z+14)(z7z+14+9z)
Apply the distributive property.
(z+2)⋅5z(7z+14)zz+2+(z+2)⋅5z(7z+14)45z(z+2)⋅5z(7z+14)z7z+14+(z+2)⋅5z(7z+14)9z
Simplify by cancelling.
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Cancel the common factor of z+2.
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Factor z+2 out of (z+2)⋅5z(7z+14).
(z+2)(5z(7z+14))zz+2+(z+2)⋅5z(7z+14)45z(z+2)⋅5z(7z+14)z7z+14+(z+2)⋅5z(7z+14)9z
Cancel the common factor.
(z+2)(5z(7z+14))zz+2+(z+2)⋅5z(7z+14)45z(z+2)⋅5z(7z+14)z7z+14+(z+2)⋅5z(7z+14)9z
Rewrite the expression.
5z(7z+14)z+(z+2)⋅5z(7z+14)45z(z+2)⋅5z(7z+14)z7z+14+(z+2)⋅5z(7z+14)9z
5z(7z+14)z+(z+2)⋅5z(7z+14)45z(z+2)⋅5z(7z+14)z7z+14+(z+2)⋅5z(7z+14)9z
Raise z to the power of 1.
5(z1z)(7z+14)+(z+2)⋅5z(7z+14)45z(z+2)⋅5z(7z+14)z7z+14+(z+2)⋅5z(7z+14)9z
Raise z to the power of 1.
5(z1z1)(7z+14)+(z+2)⋅5z(7z+14)45z(z+2)⋅5z(7z+14)z7z+14+(z+2)⋅5z(7z+14)9z
Use the power rule aman=am+n to combine exponents.
5z1+1(7z+14)+(z+2)⋅5z(7z+14)45z(z+2)⋅5z(7z+14)z7z+14+(z+2)⋅5z(7z+14)9z
Add 1 and 1.
5z2(7z+14)+(z+2)⋅5z(7z+14)45z(z+2)⋅5z(7z+14)z7z+14+(z+2)⋅5z(7z+14)9z
Cancel the common factor of 5z.
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Factor 5z out of (z+2)⋅5z(7z+14).
5z2(7z+14)+5z((z+2)(7z+14))45z(z+2)⋅5z(7z+14)z7z+14+(z+2)⋅5z(7z+14)9z
Cancel the common factor.
5z2(7z+14)+5z((z+2)(7z+14))45z(z+2)⋅5z(7z+14)z7z+14+(z+2)⋅5z(7z+14)9z
Rewrite the expression.
5z2(7z+14)+(z+2)(7z+14)⋅4(z+2)⋅5z(7z+14)z7z+14+(z+2)⋅5z(7z+14)9z
5z2(7z+14)+(z+2)(7z+14)⋅4(z+2)⋅5z(7z+14)z7z+14+(z+2)⋅5z(7z+14)9z
Cancel the common factor of 7z+14.
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Factor 7z+14 out of (z+2)⋅5z(7z+14).
5z2(7z+14)+(z+2)(7z+14)⋅4(7z+14)((z+2)⋅5z)z7z+14+(z+2)⋅5z(7z+14)9z
Cancel the common factor.
5z2(7z+14)+(z+2)(7z+14)⋅4(7z+14)((z+2)⋅5z)z7z+14+(z+2)⋅5z(7z+14)9z
Rewrite the expression.
5z2(7z+14)+(z+2)(7z+14)⋅4(z+2)⋅5z⋅z+(z+2)⋅5z(7z+14)9z
5z2(7z+14)+(z+2)(7z+14)⋅4(z+2)⋅5z⋅z+(z+2)⋅5z(7z+14)9z
Raise z to the power of 1.
5z2(7z+14)+(z+2)(7z+14)⋅4(z+2)⋅5(z1z)+(z+2)⋅5z(7z+14)9z
Raise z to the power of 1.
5z2(7z+14)+(z+2)(7z+14)⋅4(z+2)⋅5(z1z1)+(z+2)⋅5z(7z+14)9z
Use the power rule aman=am+n to combine exponents.
5z2(7z+14)+(z+2)(7z+14)⋅4(z+2)⋅5z1+1+(z+2)⋅5z(7z+14)9z
Add 1 and 1.
5z2(7z+14)+(z+2)(7z+14)⋅4(z+2)⋅5z2+(z+2)⋅5z(7z+14)9z
Cancel the common factor of z.
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Factor z out of (z+2)⋅5z(7z+14).
5z2(7z+14)+(z+2)(7z+14)⋅4(z+2)⋅5z2+z((z+2)⋅5(7z+14))9z
Cancel the common factor.
5z2(7z+14)+(z+2)(7z+14)⋅4(z+2)⋅5z2+z((z+2)⋅5(7z+14))9z
Rewrite the expression.
5z2(7z+14)+(z+2)(7z+14)⋅4(z+2)⋅5z2+(z+2)⋅5(7z+14)⋅9
5z2(7z+14)+(z+2)(7z+14)⋅4(z+2)⋅5z2+(z+2)⋅5(7z+14)⋅9
Multiply 9 by 5.
5z2(7z+14)+(z+2)(7z+14)⋅4(z+2)⋅5z2+(z+2)⋅45(7z+14)
5z2(7z+14)+(z+2)(7z+14)⋅4(z+2)⋅5z2+(z+2)⋅45(7z+14)
Simplify the numerator.
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Factor 7z+14 out of 5z2(7z+14)+(z+2)(7z+14)⋅4.
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Factor 7z+14 out of 5z2(7z+14).
(7z+14)(5z2)+(z+2)(7z+14)⋅4(z+2)⋅5z2+(z+2)⋅45(7z+14)
Factor 7z+14 out of (z+2)(7z+14)⋅4.
(7z+14)(5z2)+(7z+14)((z+2)⋅4)(z+2)⋅5z2+(z+2)⋅45(7z+14)
Factor 7z+14 out of (7z+14)(5z2)+(7z+14)((z+2)⋅4).
(7z+14)(5z2+(z+2)⋅4)(z+2)⋅5z2+(z+2)⋅45(7z+14)
(7z+14)(5z2+(z+2)⋅4)(z+2)⋅5z2+(z+2)⋅45(7z+14)
Factor 7 out of 7z+14.
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Factor 7 out of 7z.
(7(z)+14)(5z2+(z+2)⋅4)(z+2)⋅5z2+(z+2)⋅45(7z+14)
Factor 7 out of 14.
(7z+7⋅2)(5z2+(z+2)⋅4)(z+2)⋅5z2+(z+2)⋅45(7z+14)
Factor 7 out of 7z+7⋅2.
7(z+2)(5z2+(z+2)⋅4)(z+2)⋅5z2+(z+2)⋅45(7z+14)
7(z+2)(5z2+(z+2)⋅4)(z+2)⋅5z2+(z+2)⋅45(7z+14)
Apply the distributive property.
7(z+2)(5z2+z⋅4+2⋅4)(z+2)⋅5z2+(z+2)⋅45(7z+14)
Move 4 to the left of z.
7(z+2)(5z2+4⋅z+2⋅4)(z+2)⋅5z2+(z+2)⋅45(7z+14)
Multiply 2 by 4.
7(z+2)(5z2+4z+8)(z+2)⋅5z2+(z+2)⋅45(7z+14)
7(z+2)(5z2+4z+8)(z+2)⋅5z2+(z+2)⋅45(7z+14)
Simplify the denominator.
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Factor (z+2)⋅5 out of (z+2)⋅5z2+(z+2)⋅45(7z+14).
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Factor (z+2)⋅5 out of (z+2)⋅5z2.
7(z+2)(5z2+4z+8)(z+2)⋅5(z2)+(z+2)⋅45(7z+14)
Factor (z+2)⋅5 out of (z+2)⋅45(7z+14).
7(z+2)(5z2+4z+8)(z+2)⋅5(z2)+(z+2)⋅5(9(7z+14))
Factor (z+2)⋅5 out of (z+2)⋅5(z2)+(z+2)⋅5(9(7z+14)).
7(z+2)(5z2+4z+8)(z+2)⋅5(z2+9(7z+14))
7(z+2)(5z2+4z+8)(z+2)⋅5(z2+9(7z+14))
Apply the distributive property.
7(z+2)(5z2+4z+8)(z+2)⋅5(z2+9(7z)+9⋅14)
Multiply 7 by 9.
7(z+2)(5z2+4z+8)(z+2)⋅5(z2+63z+9⋅14)
Multiply 9 by 14.
7(z+2)(5z2+4z+8)(z+2)⋅5(z2+63z+126)
7(z+2)(5z2+4z+8)(z+2)⋅5(z2+63z+126)
Cancel the common factor of z+2.
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Cancel the common factor.
7(z+2)(5z2+4z+8)(z+2)⋅5(z2+63z+126)
Rewrite the expression.
7(5z2+4z+8)5(z2+63z+126)
7(5z2+4z+8)5(z2+63z+126)
Divide (z/(z+2)+4/(5z))/(z/(7z+14)+9/z)

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