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\frac{9x^{2}}{1296}-\frac{16y^{2}}{1296}-1
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 144 and 81 is 1296. Multiply \frac{x^{2}}{144} times \frac{9}{9}. Multiply \frac{y^{2}}{81} times \frac{16}{16}.
\frac{9x^{2}-16y^{2}}{1296}-1
Since \frac{9x^{2}}{1296} and \frac{16y^{2}}{1296} have the same denominator, subtract them by subtracting their numerators.
\frac{9x^{2}-16y^{2}}{1296}-\frac{1296}{1296}
To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{1296}{1296}.
\frac{9x^{2}-16y^{2}-1296}{1296}
Since \frac{9x^{2}-16y^{2}}{1296} and \frac{1296}{1296} have the same denominator, subtract them by subtracting their numerators.
\frac{9x^{2}-16y^{2}-1296}{1296}
Factor out \frac{1}{1296}.