Question

$\frac{4}{b - 3 } = \frac{6}{x}$
what is the value of x interm of b ?​

Answer 1

We have studied procedures for working with fractions in earlier grades.

   ab×cd=acbd(b≠0;d≠0)

   ab+cb=a+cb(b≠0)

   ab÷cd=ab×dc=adbc(b≠0;c≠0;d≠0)

Note: dividing by a fraction is the same as multiplying by the reciprocal of the fraction.

In some cases of simplifying an algebraic expression, the expression will be a fraction. For example,

x2+3xx+3

has a quadratic binomial in the numerator and a linear binomial in the denominator. We have to apply the different factorisation methods in order to factorise the numerator and the denominator before we can simplify the expression.

x2+3xx+3=x(x+3)x+3=x(x≠−3)

If x=−3 then the denominator, x+3=0 and the fraction is undefined.

This video shows some examples of simplifying fractions.

Video: 2DNV

Worked example 18: Simplifying fractions

Simplify: ax−b+x−abax2−abx,(x≠0;x≠b)

Use grouping to factorise the numerator and take out the common factor ax in the denominator (ax−ab)+(x−b)ax2−abx=a(x−b)+(x−b)ax(x−b)

Take out common factor (x−b) in the numerator =(x−b)(a+1)ax(x−b)

Cancel the common factor in the numerator and the denominator to give the final answer =a+1ax

Worked example 19: Simplifying fractions

Simplify: x2−x−2x2−4÷x2+xx2+2x,(x≠0;x≠±2)

Factorise the numerator and denominator =(x+1)(x−2)(x+2)(x−2)÷x(x+1)x(x+2)

Change the division sign and multiply by the reciprocal =(x+1)(x−2)(x+2)(x−2)×x(x+2)x(x+1)

Write the final answer =1Step-by-step explanation:

Answer 2

$\huge{\mathfrak{\blue{\underline{Answer}}}}$

The value of X in terms of b

$\frac{4}{b - 3 } = \frac{6}{x} \\ ................ \\ 4x = 6b - 18$

$x = \frac{6b - 18}{4} \\ x = \frac{2(3b - 9)}{4}$

$\huge{\mathfrak{\blue{\underline{x=3b-9/2}}}}$