Brain Easier

Algebra Level 2

(x+5)/(x-6) = (x-1)/(x+2) , then find the value of x?

-3/7 2/7 3/7 -2/7

2 solutions

Shreya Jain
Sep 20, 2015

using componendo/ dividendo:

(x+5)/(x-6) = (x-1)/(x+2) or (x+5-x+6)/(x-6) = (x-1-x-2)/(x+2) or (11)/(x-6) = (-3)/(x+2) or 11x+4= -3x or 14x=4 or x=-2/7

hence, x=(-2/7)

Phu Tuan Lo
May 17, 2015

This should've been written as (x+5)/(x-6) = (x-1)/(x+2)

Dude, this problem has two solutions. 2/7 and -2/7.

$\frac { x+5 }{ x-6 } =\frac { x-1 }{ x+2 }$

$(x+5)(x+2)=(x-6)(x-1)$

${ x }^{ 2 }+7x+10={ x }^{ 2 }-7x+6$

$14x+4=0$ or $-14x-4=0$

$x=\frac { 2 }{ 7 }$ or $x=-\frac { 2 }{ 7 }$

The AdamMZ - 5 years, 11 months ago

(x+5)/(x-6)=(x-1)(x+2)

(x+5)(x+2)=(x-6)(x-1)

x^2+7x+10=x^2-7x+6

take out x^2, move either the positive 7x and 6 or negative 7x and 10

choice 1: 10-6=-7x-7x

4=-14x

x=-2/7

choice 2:

7x+7x=6-10

14x=-4

x=-2/7

there is only one solution to this because x^2 has been taken out, therefore x=2/7 is an erroneous solution

Caeo Tan - 5 years, 10 months ago

I finally found my mistake. :P

$14x+4=0$

$14x=-4$

$x=\frac{-4}{14}$

$x=-\frac{4}{14}$

Oh dear. Sorry for the trouble.

The AdamMZ - 5 years, 10 months ago