If x=4a y=3 and z=1, simplify : 2x+3y-x+2y 4x-y/z

Mathematics

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Answer

4a+1516a3\dfrac{4a + 15}{16a - 3}

Step 1: Simplify the numerator.

2x+3yx+2y2x + 3y - x + 2y

=(2xx)+(3y+2y)= (2x - x) + (3y + 2y)

=x+5y= x + 5y

Step 2: The expression is now

x+5y4xyz\frac{x + 5y}{4x - \frac{y}{z}}

Step 3: Substitute x=4ax = 4a, y=3y = 3, z=1z = 1 into the numerator.

x+5y=4a+5(3)x + 5y = 4a + 5(3)

=4a+15= 4a + 15

Step 4: Substitute into the denominator.

4xyz=4(4a)314x - \frac{y}{z} = 4(4a) - \frac{3}{1}

=16a3= 16a - 3

Step 5: The simplified expression is

4a+1516a3\frac{4a + 15}{16a - 3}

4a+1516a3\boxed{\dfrac{4a + 15}{16a - 3}}

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