Question

How do you simplify $\dfrac{6}{{X - 1}} = \dfrac{4}{{X + 1}}$?

Answer 1

Hint: In this question, the algebraic expression is given and we have to simplify the expression. The expression is in the form of a fraction. To solve the fraction, we have to follow the below steps.
1. Apply the cross-multiplication.
2. Apply the distributive property to remove the brackets.
3. Isolate the variable.
4. Simplify the expression.

Complete step by step answer:
In this question, the given algebraic expression is:
$ \Rightarrow \dfrac{6}{{X - 1}} = \dfrac{4}{{X + 1}}$
The first step is to apply the cross-multiplication. The cross multiplies the fraction means multiplying the opposite numerators and denominators of equivalent fractions.
$ \Rightarrow 6\left( {X + 1} \right) = 4\left( {X - 1} \right)$
The second step is to apply the distributive property to remove the brackets.
$ \Rightarrow 6X + 6 = 4X - 4$
The third step is to isolate the variable.
For that, let us subtract 4X on both sides.
$ \Rightarrow 6X - 4X + 6 = 4X - 4X - 4$
The subtraction of 6x and 4x is 2x on the left-hand side. The subtraction of 4x and 4x is 0 on the right-hand side.
That is equal to,
$ \Rightarrow 2X + 6 = - 4$
Now, let us subtract -6 on both sides.
$ \Rightarrow 2X + 6 - 6 = - 4 - 6$
The subtraction of 6 and 6 is 0 on the left-hand side. The subtraction of -4 and 6 is -10 on the right-hand side.
That is equal to,
$ \Rightarrow 2X = - 10$
The next step is to simplify the expression.
Let us divide both sides by 2.
$ \Rightarrow \dfrac{{2X}}{2} = \dfrac{{ - 10}}{2}$
The division of 2 and 2 is 1 on the left-hand side. The division of -10 and 2 is -5 on the right-hand side.
That is equal to,
$ \Rightarrow X = - 5$

So, the correct answer is “-5”.

Note: We can verify the answer by putting the value of x in the given expression.
The given expression is:
$ \Rightarrow \dfrac{6}{{X - 1}} = \dfrac{4}{{X + 1}}$
Let us put the value of X as -5.
$ \Rightarrow \dfrac{6}{{ - 5 - 1}} = \dfrac{4}{{ - 5 + 1}}$
That is equal to,
$ \Rightarrow \dfrac{6}{{ - 6}} = \dfrac{4}{{ - 4}}$
Let us apply division on both sides.
$ \Rightarrow - 1 = - 1$
Hence, the answer we get is correct.