If \(4^x - 4^{x-1} = 48\), then the value of \(\frac{2x-1}{2x+3}\) is:
\(\frac{5}{9}\)
Factor out \(4^{x-1}\): \(4^{x-1}(4 - 1) = 48\).
This gives \(4^{x-1} = 16 = 4^2\), so \(x - 1 = 2\), i.e. \(x = 3\).
Substituting \(x = 3\): \(\frac{2x-1}{2x+3} = \frac{2(3)-1}{2(3)+3} = \frac{5}{9}\).
Hence, the value of \(\frac{2x-1}{2x+3}\) is \(\frac{5}{9}\).
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Important Questions from Algebric Equations
If m + n = 24, then (m - 16)³ + (n - 8)³ is ____.
For the following equations, what are the values of a and b to have infinitely many solutions?
ax + by = 2
3x - (5 - 2ay) = 6
If m + n = 24, then (m - 16)³ + (n - 8)³ is ____.
For the following equations, what are the values of a and b to have infinitely many solutions?
ax + by = 2
3x - (5 - 2ay) = 6
Simplify the following expression:
\(\frac{(x - y)^3 + (y - z)^3 + (z - x)^3}{(x - y)(y - z)(z - x)}\)
