Nice Simplification

Algebra Level 1

Simplify 5 x + 5 x + 1 5 x − 1 + 5 x \large \frac{5^x +5^{x+1}}{5^{x-1}+5^x}


The answer is 5.

Hana Wehbi by Hana Wehbi , 51, USA

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

Munem Shahriar
Jan 28, 2018

5 x + 5 x + 1 5 x − 1 + 5 x \dfrac{5^x+ 5^{x+1}}{5^{x-1} + 5^x}

= 5 x + 5 x × 5 1 5 x × 5 − 1 + 5 x = \dfrac{5^x + 5^x \times 5^1}{5^x \times 5^{-1} + 5^x}

= 5 x × 6 5 x ( 1 + 1 5 ) = \dfrac{5^x \times 6}{5^x \left(1 + \dfrac 15\right)}

= 6 6 5 = \dfrac 6{ \frac 65}

= 6 × 5 6 = \dfrac{6 \times 5}{6}

= 5 = \boxed 5

5 Helpful 0 Interesting 0 Brilliant 0 Confused

Thank you.

Hana Wehbi - 3 years, 4 months ago

I used the same method with a difference that I took 5^x = a.

Aryan Sanghi - 3 years, 4 months ago
Chew-Seong Cheong
Feb 10, 2018

5 x + 5 x + 1 5 x − 1 + 5 x = 5 x ( 1 + 5 ) 5 x − 1 ( 1 + 5 ) = 5 x 5 x − 1 = 5 \dfrac {5^x+5^{x+1}}{5^{x-1}+5^x} = \dfrac {5^x(1+5)}{5^{x-1}(1+5)} = \dfrac {5^x}{5^{x-1}} = \boxed{5}

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Thank you for sharing your solution.

Hana Wehbi - 3 years, 4 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...