Math

Question Find the excluded value for the rational function y=6x+19x4y=\frac{6 x+1}{9 x-4}.

Studdy Solution

STEP 1

1. The expression y=6x+19x4y=\frac{6x+1}{9x-4} is a rational function, where xx and yy are real numbers.
2. An excluded value for xx occurs when the denominator of the rational function is equal to zero, as division by zero is undefined.

STEP 2

1. Identify the denominator of the rational function.
2. Set the denominator equal to zero to find the excluded value for xx.
3. Solve for the excluded value.

STEP 3

Identify the denominator of the rational function y=6x+19x4y=\frac{6x+1}{9x-4}.
The denominator is 9x49x-4.

STEP 4

Set the denominator equal to zero to find the excluded value for xx.
9x4=0 9x - 4 = 0

STEP 5

Solve the equation for xx to find the excluded value.
9x=4 9x = 4

STEP 6

Divide both sides of the equation by 9 to isolate xx.
x=49 x = \frac{4}{9}
The excluded value for xx is 49\frac{4}{9}, as this value would make the denominator of the rational function zero, which is undefined.

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