If a number is added to the numerator of [tex]\frac{4}{9}[/tex] and the same number is subtracted from the denominator, the result is [tex]-9[/tex]. Find the number.

What a delightful little problem !
You said that ** (4 + x) / (9 - x) = -9**
Multiply each side by (9 - x) : (4 + x) = -9 (9 - x)
Eliminate parentheses: 4 + x = -81 + 9x
Add 81 to each side: 85 + x = 9x
Subtract 'x' from each side: 85 = 8x
Divide each side by 8 : ***85/8 = x *** (or 10.625)

Answered by AL2006 | 2024-06-10

(4+n)/(9-n)=-9
4+n=-9(9-n)
4+n=-81+9n
4+81=9n-n
85=8n
n=85/8=80/8+5/8=10+5/8

Answered by Anonymous | 2024-06-10

The number that is added to the numerator and subtracted from the denominator is 8 85 ​ , which equals 10.625.
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Answered by AL2006 | 2024-12-26