Question

Simplify and solve the equation 1/a+2+1/a+1=2/a+10

Answer 1

Answer:

a=7

Step-by-step explanation:

1/a+2+1/a+1=2/a+10

1/a+1/a-2/a=-2-1+10

2-2/a=7

1/a=7

a=7

Answer 2

The equation has no solution

Solution:

Given that,

$\frac{1}{a} + 2 + \frac{1}{a} + 1 = \frac{2}{a} + 10$

We have to simplify and solve the equation

Solve for "a"

From given,

$\frac{1}{a} + 2 + \frac{1}{a} + 1 = \frac{2}{a} + 10$

$\mathrm{Subtract\:}2+1\mathrm{\:from\:both\:sides}\\\\\frac{1}{a}+2+\frac{1}{a}+1-\left(2+1\right)=\frac{2}{a}+10-\left(2+1\right)\\\\\mathrm{Simplify}\\\\\frac{1}{a}+\frac{1}{a}=\frac{2}{a}+7\\\\\mathrm{Multiply\:both\:sides\:by\:}a\\\\\frac{1}{a}a+\frac{1}{a}a=\frac{2}{a}a+7a$

$\mathrm{Simplify}\\\\1+1=2+7a\\\\2 = 2 + 7a\\\\\mathrm{Subtract\:}2\mathrm{\:from\:both\:sides}\\\\2 - 2 = 2 + 7a - 2\\\\7a = 0$

a = 0

But in,

$\frac{1}{a} + 2 + \frac{1}{a} + 1 = \frac{2}{a} + 10$

"a" cannot be zero, because if a = 0, then equation is undefined

Thus, the equation has no solution

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