Simplify a fraction

Algebra Level 2

Simplify 3 x + 63 2 1 x − 2 + 7 x − 1 \frac{3^x+63}{21^{x-2}+7^{x-1}}

3 7 x \frac{3}{7^x} 21 7 x \frac{21}{7^x} 441 7 x \frac{441}{7^x} 9 7 x \frac{9}{7^x} 63 7 x \frac{63}{7^x}

Klement Chua by Klement Chua , 15, Singapore

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2 solutions

3 x + 63 2 1 x − 2 + 7 x − 1 = 9 ( 3 x − 2 + 7 ) 7 x − 2 ( 3 x − 2 + 7 ) = 9 × 7 2 7 x − 2 + 2 = 441 7 x \frac {3^x+63}{21^{x-2}+7^{x-1}} = \frac {9\cancel{(3^{x-2}+7)}}{7^{x-2}\cancel{(3^{x-2}+7)}} = \frac {9 \times 7^2}{7^{x-2+2}} = \boxed{\frac {441}{7^x}}

3 Helpful 1 Interesting 3 Brilliant 0 Confused

@Klement Chua , since you ask to simplify the expression, 441 441 is simpler than 9 × 49 9 \times 49 . It also make the problem slightly more challenging.

Chew-Seong Cheong - 1 month ago

Ah yes, thank you so much for correcting my error! @Chew-Seong Cheong

Klement Chua - 1 month ago
Razing Thunder
May 24, 2021

step by step solution

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