Question

find the equation: 2 ( \frac { 3 x - 5 } { x + 2 } ) - 5 ( \frac { x + 2 } { 3 x - 5 } ) = 3 , x \neq - 2 x \neq \frac { 5 } { 3 }​

Answer 1

First, we have to find the lowest common denominator (LCD)

We recognize, that three of the denominators are multiples of (x-5)

x-5

2x-10=2(x-5)

6x-30= 6(x-5)

Now, we see, that 6(x-5) is their LCD.

We summarize these three fractions.

6x6(x−5)+3∗36(x−5)−1−x6(x−5)

=6x+9–1+x6(x−5)=7x+86(x−5)

When we look at the last fraction, we see, that its denominator is a multiple of three:

15–3x=3(5-x)

Now we change the sign:

(5-x)=-(x-5)

We get:

15–3x=-3(5-x)

The entire fraction is:

7−3(x−5)=−73(x−5)=146(x−5)

7x+86(x−5)−146(x−5)=7x−66(x−5)=1

Now, we multiply by 6(x+5)

7x-6=6(x+5)

7x-6=6x+30

We subtract 6x and add 6 on both sides:

x=36

Step-by-step explanation:

hope its will help yoy