Question

plz solve this one
solve the following equations:
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Answer 1

Answer:

x=3/2

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

we get,

                           $\frac{1}{x-1}+\frac{2}{x-2}-\frac{3}{x-3}=0$

After simplifying,

we get,$\frac{(x-2)*2(x-1)}{(x-1)(x-2)} = \frac{3x-4}{(x-1)(x-2)}$

again simplifying,

we get,$\frac{(3x-4)}{(x-1)(x-2)} - \frac{3}{x-3} = 0$

again simplifying,

we get,$\frac{(3x-4)(x-3)-(3(x-1)(x-2))}{(x-1)(x-2)(x-3)}=\frac{6-4x}{(x-1)(x-2)(x-3)}$

Pulling out like factors:

$6-4x=-2(2x-3)$

We get the equation,

$\frac{-2(2x-3)}{(x-1)(x-2)(x-3)}=0$

When a fraction is equal to zero:

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now, to get rid of the denominator, Tiger multiplies both sides of the equation by the denominator.

Here's how:

$\frac{-2(2x-3)}{(x-1)(x-2)(x-3)}(x-1)(x-2)(x-3)=0 (x-1)(x-2)(x-3)$

Now, on the left-hand side, the  (x-1) • (x-2) • (x-3)  cancels out the denominator, while, on the right-hand side, zero times anything is still zero.

The equation now becomes,

$-2(2x-3)=0$

Solve: -2=0

The equation has no solution

A non-zero constant never equals zero.

SOLVING A SINGLE VARIABLE EQUATION:

Solve: $2x-3=0$

Add 3 to both sides of the equation :

           $2x=3$

Divide both sides of the equation by 2 :

           $x=\frac{3}{2}$

           $x=1.5$

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Answer 2

Answer:

x=3/2

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

we get,

\frac{1}{x-1}+\frac{2}{x-2}-\frac{3}{x-3}=0

x−1

1

+

x−2

2

−

x−3

3

=0

After simplifying,

we get,\frac{(x-2)*2(x-1)}{(x-1)(x-2)} = \frac{3x-4}{(x-1)(x-2)}

(x−1)(x−2)

(x−2)∗2(x−1)

=

(x−1)(x−2)

3x−4

again simplifying,

we get,\frac{(3x-4)}{(x-1)(x-2)} - \frac{3}{x-3} = 0

(x−1)(x−2)

(3x−4)

−

x−3

3

=0

again simplifying,

we get,\frac{(3x-4)(x-3)-(3(x-1)(x-2))}{(x-1)(x-2)(x-3)}=\frac{6-4x}{(x-1)(x-2)(x-3)}

(x−1)(x−2)(x−3)

(3x−4)(x−3)−(3(x−1)(x−2))

=

(x−1)(x−2)(x−3)

6−4x

Pulling out like factors:

6-4x=-2(2x-3)6−4x=−2(2x−3)

We get the equation,

\frac{-2(2x-3)}{(x-1)(x-2)(x-3)}=0

(x−1)(x−2)(x−3)

−2(2x−3)

=0

When a fraction is equal to zero:

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now, to get rid of the denominator, Tiger multiplies both sides of the equation by the denominator.

Here's how:

\frac{-2(2x-3)}{(x-1)(x-2)(x-3)}(x-1)(x-2)(x-3)=0 (x-1)(x-2)(x-3)

(x−1)(x−2)(x−3)

−2(2x−3)

(x−1)(x−2)(x−3)=0(x−1)(x−2)(x−3)

Now, on the left-hand side, the (x-1) • (x-2) • (x-3) cancels out the denominator, while, on the right-hand side, zero times anything is still zero.

The equation now becomes,

-2(2x-3)=0−2(2x−3)=0

Solve: -2=0

The equation has no solution

A non-zero constant never equals zero.

SOLVING A SINGLE VARIABLE EQUATION:

Solve: 2x-3=02x−3=0

Add 3 to both sides of the equation :

2x=32x=3

Divide both sides of the equation by 2 :

x=\frac{3}{2}x=

2

3

x=1.5x=1.5

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