What is (2^{x+3}+2^{x+4})/(2^{x+5)-2^{x+2}} ?

The solution to (2^{x+3}+2^{x+4})/(2^{x+5)-2^{x+2}} is 6/7

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simplify (2^{x+3}+2^{x+4})/(2^{x+5)-2^{x+2}}

simplify

\frac{2 ^{x + 3} + 2 ^{x + 4}}{2 ^{x + 5} - 2 ^{x + 2}}

\frac{6}{7}

Decimal Notation

0.85714 \dots

Solution steps

\frac{2 ^{x + 3} + 2 ^{x + 4}}{2 ^{x + 5} - 2 ^{x + 2}}

Factor

2^{x + 3} + 2^{x + 4} : 3 \cdot 2^{3 + x}

= \frac{3 \cdot 2 ^{3 + x}}{2 ^{x + 5} - 2 ^{x + 2}}

Factor

2^{x + 5} - 2^{x + 2} : 7 \cdot 2^{2 + x}

= \frac{3 \cdot 2 ^{3 + x}}{7 \cdot 2 ^{2 + x}}

Cancel

\frac{3 \cdot 2 ^{3 + x}}{7 \cdot 2 ^{2 + x}} : \frac{3 \cdot 2}{7}

= \frac{3 \cdot 2}{7}

Multiply the numbers:

3 \cdot 2 = 6

= \frac{6}{7}

3^{6} \cdot 5^{4}

lo g_{3} (108) - lo g_{3} (4)

\frac{4}{x + 2} + \frac{5}{x - 3}

(9 mn - 19 m^{4} n) - (8 m^{2} + 12 m^{4} n + 9 mn)

2 x^{2} \cdot 3 x^{2}

What is (2^{x+3}+2^{x+4})/(2^{x+5)-2^{x+2}} ?
The solution to (2^{x+3}+2^{x+4})/(2^{x+5)-2^{x+2}} is 6/7