\frac{4}{b - 3 } = \frac{6}{x}b−34=x6
what is the value of x interm of b ?
Answers
Answer:
A rational expression is a ratio of two polynomials. A rational expression is considered simplified if the numerator and denominator have no factors in common.
If this is new to you, we recommend that you check out our intro to simplifying rational expressions.
What you will learn in this lesson
In this lesson, you will practice simplifying more complicated rational expressions. Let's look at two examples, and then you can try some problems!
Example 1: Simplifying 10x32x2−18x~\dfrac{10x^3}{2x^2-18x} 2x2−18x10x3space, start fraction, 10, x, cubed, divided by, 2, x, squared, minus, 18, x, end fraction
Step 1: Factor the numerator and denominator
Here it is important to notice that while the numerator is a monomial, we can factor this as well.
10x32x2−18x=2⋅5⋅x⋅x22⋅x⋅(x−9)\dfrac{10x^3}{2x^2-18x}=\dfrac{ 2\cdot 5\cdot x\cdot x^2}{ 2\cdot x\cdot (x-9)}2x2−18x10x3=2⋅x⋅(x−9)2⋅5⋅x⋅x2start fraction, 10, x, cubed, divided by, 2, x, squared, minus, 18, x, end fraction, equals, start fraction, 2, dot, 5, dot, x, dot, x, squared, divided by, 2, dot, x, dot, left parenthesis, x, minus, 9, right parenthesis, end fraction
Step 2: List restricted values
From the factored form, we see that x≠0{x\neq0}x=0x, does not equal, 0 and x≠9{x\neq9}x=9x, does not equal, 9.
Step 3: Cancel common factors
2⋅5⋅x⋅x22⋅x⋅(x−9)=2⋅5⋅x⋅x22⋅x⋅(x−9)=5x2x−9\begin{aligned}\dfrac{ \tealD 2\cdot 5\cdot \purpleC{x}\cdot x^2}{ \tealD 2\cdot \purpleC{x}\cdot (x-9)}&=\dfrac{ \tealD{\cancel{ 2}}\cdot 5\cdot \purpleC{\cancel{x}}\cdot x^2}{ \tealD{\cancel{ 2}}\cdot \purpleC{\cancel{x}}\cdot (x-9)}\\ \\ &=\dfrac{5x^2}{x-9} \end{aligned}2⋅x⋅(x−9)2⋅5⋅x⋅x2=2
⋅x
⋅(x−9)2
⋅5⋅x
⋅x2=x−95x2
Step 4: Final answer
We write the simplified form as follows:
5x2x−9\dfrac{5x^2}{x-9}x−95x2start fraction, 5, x, squared, divided by, x, minus, 9, end fraction for x≠0x\neq 0x=0x, does not equal, 0
[Why do we require x≠0?]
Step-by-step explanation: