# Evaluate ((7/24)-(-9/8))/(1+(7/24)(-9/8))

(724)-(-98)1+(724)(-98)
Multiply the numerator and denominator of the complex fraction by 24.
Multiply (724)-(-98)1+(724)(-98) by 2424.
2424⋅(724)-(-98)1+(724)(-98)
Combine.
24((724)-(-98))24(1+(724)(-98))
24((724)-(-98))24(1+(724)(-98))
Apply the distributive property.
24(724)+24(-(-98))24⋅1+24((724)(-98))
Cancel the common factor of 24.
Cancel the common factor.
24(724)+24(-(-98))24⋅1+24((724)(-98))
Rewrite the expression.
7+24(-(-98))24⋅1+24((724)(-98))
7+24(-(-98))24⋅1+24((724)(-98))
Simplify the numerator.
Multiply -(-98).
Multiply -1 by -1.
7+24(1(98))24⋅1+24((724)(-98))
Multiply 98 by 1.
7+24(98)24⋅1+24((724)(-98))
7+24(98)24⋅1+24((724)(-98))
Cancel the common factor of 8.
Factor 8 out of 24.
7+8(3)9824⋅1+24((724)(-98))
Cancel the common factor.
7+8⋅39824⋅1+24((724)(-98))
Rewrite the expression.
7+3⋅924⋅1+24((724)(-98))
7+3⋅924⋅1+24((724)(-98))
Multiply 3 by 9.
7+2724⋅1+24((724)(-98))
3424⋅1+24((724)(-98))
3424⋅1+24((724)(-98))
Simplify the denominator.
Multiply 24 by 1.
3424+24((724)(-98))
Cancel the common factor of 3.
Move the leading negative in -98 into the numerator.
3424+24(724⋅-98)
Factor 3 out of 24.
3424+24(73(8)⋅-98)
Factor 3 out of -9.
3424+24(73⋅8⋅3⋅-38)
Cancel the common factor.
3424+24(73⋅8⋅3⋅-38)
Rewrite the expression.
3424+24(78⋅-38)
3424+24(78⋅-38)
Multiply 78 and -38.
3424+247⋅-38⋅8
Multiply 7 by -3.
3424+24-218⋅8
Multiply 8 by 8.
3424+24(-2164)
Cancel the common factor of 8.
Factor 8 out of 24.
3424+8(3)-2164
Factor 8 out of 64.
3424+8⋅3-218⋅8
Cancel the common factor.
3424+8⋅3-218⋅8
Rewrite the expression.
3424+3(-218)
3424+3(-218)
Combine 3 and -218.
3424+3⋅-218
Multiply 3 by -21.
3424+-638
Move the negative in front of the fraction.
3424-638
To write 24 as a fraction with a common denominator, multiply by 88.
3424⋅88-638
Combine 24 and 88.
3424⋅88-638
Combine the numerators over the common denominator.
3424⋅8-638
Simplify the numerator.
Multiply 24 by 8.
34192-638
Subtract 63 from 192.
341298
341298
341298
Multiply the numerator by the reciprocal of the denominator.
34(8129)
Multiply 34(8129).
Combine 34 and 8129.
34⋅8129
Multiply 34 by 8.
272129
272129
The result can be shown in multiple forms.
Exact Form:
272129
Decimal Form:
2.10852713…
Mixed Number Form:
214129
Evaluate ((7/24)-(-9/8))/(1+(7/24)(-9/8))

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