Question

WILL GIVE BRAINLIEST !!!!Simplify 1 over quantity x minus 3 plus 4 over x all over 4 over x minus 1 over quantity x minus 3. 

Answer 1

Answer:

$\frac{5x-12}{3x-12}$

Explanation:

We are given the expression

$\frac{\frac{1}{x-3}+\frac{4}{x}}{\frac{4}{x}-\frac{1}{x-3}}$

We will start out simplifying the numerator.  To do this, we will multiply both terms by (x-3) to cancel this denominator:

$\frac{\frac{1\times (x-3)}{x-3}+\frac{4\times (x-3)}{x}}{\frac{4}{x}-\frac{1}{x-3}}\\\\\\=\frac{1+\frac{4(x-3)}{x}}{\frac{4}{x}-\frac{1}{x-3}}$

Next we will cancel the denominator of x in the numerator of the expression by multiplying everything in the numerator by x:

$\frac{1\times x +\frac{4(x-3)\times x}{x}}{\frac{4}{x}-\frac{1}{x-3}}\\\\\\=\frac{x+4(x-3)}{\frac{4}{x}-\frac{1}{x-3}}$

Using the distributive property on the numerator, we have

$\frac{x+4x-12}{\frac{4}{x}-\frac{1}{x-3}}$

Combining like terms gives us

$\frac{5x-12}{\frac{4}{x}-\frac{1}{x-3}}$

Following a similar process for the denominator,multiply both terms by (x-3):

$\frac{5x-12}{\frac{4\times (x-3)}{x}-\frac{1\times (x-3)}{x-3}}\\\\\\=\frac{5x-12}{\frac{4(x-3)}{x}-1}$

Now multiply both terms in the denominator by x:

$\frac{5x-12}{\frac{4(x-3)\times x}{x}-1\times x}\\\\\\=\frac{5x-12}{4(x-3)-x}$

Using the distributive property on the denominator, we have

$\frac{5x-12}{4x-12-x}$

Combining like terms, we have

$\frac{5x-12}{3x-12}$