Question

simplif the bionomials (2/3x+4) (3/2x+6) - (1/7x +1 )

Answer 1

(2x/3+4)(3x/2+6)(1/7x+1)(1/7x-1)
Final result :
(x + 6) • (x + 4) • (x + 7) • (x - 7)
—————————————————————————————————————
49
Step by step solution :
Step 1 :
1
Simplify —
7
Equation at the end of step 1 :
x x 1 1
((((2•—)+4)•((3•—)+6))•((—•x)+1))•((—•x)-1)
3 2 7 7
Step 2 :
Rewriting the whole as an Equivalent Fraction :
2.1 Subtracting a whole from a fraction

Rewrite the whole as a fraction using 7 as the denominator :

1 1 • 7
1 = — = —————
1 7
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :
2.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

x - (7) x - 7
——————— = —————
7 7
Equation at the end of step 2 :
x x 1 (x-7)
((((2•—)+4)•((3•—)+6))•((—•x)+1))•—————
3 2 7 7
Step 3 :
1
Simplify —
7
Equation at the end of step 3 :
x x 1 (x-7)
((((2•—)+4)•((3•—)+6))•((—•x)+1))•—————
3 2 7 7
Step 4 :
Rewriting the whole as an Equivalent Fraction :
4.1 Adding a whole to a fraction

Rewrite the whole as a fraction using 7 as the denominator :

1 1 • 7
1 = — = —————
1 7
Adding fractions that have a common denominator :
4.2 Adding up the two equivalent fractions

x + 7 x + 7
————— = —————
7 7
Equation at the end of step 4 :
x x (x+7) (x-7)
((((2•—)+4)•((3•—)+6))•—————)•—————
3 2 7 7
Step 5 :
x
Simplify —
2
Equation at the end of step 5 :
x x (x+7) (x-7)
((((2•—)+4)•((3•—)+6))•—————)•—————
3 2 7 7
Step 6 :
Rewriting the whole as an Equivalent Fraction :
6.1 Adding a whole to a fraction

Rewrite the whole as a fraction using 2 as the denominator :

6 6 • 2
6 = — = —————
1 2
Adding fractions that have a common denominator :
6.2 Adding up the two equivalent fractions

3x + 6 • 2 3x + 12
—————————— = ———————
2 2
Equation at the end of step 6 :
x (3x+12) (x+7) (x-7)
((((2•—)+4)•———————)•—————)•—————
3 2 7 7
Step 7 :
x
Simplify —
3
Equation at the end of step 7 :
x (3x+12) (x+7) (x-7)
((((2•—)+4)•———————)•—————)•—————
3 2 7 7
Step 8 :
Rewriting the whole as an Equivalent Fraction :
8.1 Adding a whole to a fraction

Rewrite the whole as a fraction using 3 as the denominator :



4 4 • 3
4 = — = —————
1 3
Adding fractions that have a common denominator :
8.2 Adding up the two equivalent fractions

2x + 4 • 3 2x + 12
—————————— = ———————
3 3
Equation at the end of step 8 :
(2x + 12) (3x + 12) (x + 7) (x - 7)
((————————— • —————————) • ———————) • ———————
3 2 7 7
Step 9 :
Step 10 :
Pulling out like terms :
10.1 Pull out like factors :

2x + 12 = 2 • (x + 6)

Step 11 :
Pulling out like terms :
11.1 Pull out like factors :

(3x + 12) = 3 • (x + 4)

Equation at the end of step 11 :
(x + 7) (x - 7)
((x + 6) • (x + 4) • ———————) • ———————
7 7
Step 12 :
Equation at the end of step 12 :
(x + 6) • (x + 4) • (x + 7) (x - 7)
————————— • ———————
7 7

Step  13  :

Final result :

(x + 6) • (x + 4) • (x + 7) • (x - 7) ————————————————————————————————————— 49

Answer 2

Heyy Friend ✌
Here is u r Ans ➡

$= (\frac{2}{ 3x} + 4)( \frac{3}{2x} + 6) - ( \frac{1}{7x } + 1)$

$= \frac{2 + 12x}{3x} \times \frac{3 + 12x}{2x} - \frac{1}{2x} - 1$

$= \frac{2(1 + 6 x) }{3x} \times \frac{3(1 + 4x)}{2x} - \frac{1}{2x} - 1$

$= \frac{1 + 6x}{x} \times \frac{1 + 4x}{x} - \frac{1}{2x} - 1$

$= \frac{(1 + 6x) \times (1 + 4x)}{x {}^{2} } - \frac{1}{2x} - 1$

$= \frac{1 + 4x + 6x + 24x {}^{2} }{x {}^{2} } - \frac{1}{2x} - 1$

$= \frac{1 + 10x + 24x {}^{2} }{x {}^{2} } - \frac{1}{2x} - 1$
$= \frac{2(10x + 24x {}^{2} ) - x - 2x {}^{2} }{2x {}^{2} }$


$= \frac{2 + 20x + 48x {}^{2} - x - 2x {}^{2} }{2x {}^{2} }$

$= \frac{2 + 19x + 46x {}^{2} }{2x {}^{2} }$

$= \frac{46x {}^{2} + 19x + 2}{2x {}^{2} }$
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